Analysis
Grenzwerte, Ableitungen, Optimierung und Funktionsverhalten.
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1. $f(x) = 2^x$ | $x$ | $f(x)$ | | --- | --- | | $-2$ | | | $-1$ | | | …
The filled table is as above with \( f(-2)=\frac{1}{4} \), \( f(-1)=\frac{1}{2} \), \( f(0) = 1 \), \( f(1)=2 \), \( f(2)=4 \).
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use the graphs of f and g to evaluate the composite function, (g ∘ f)(6…
$-6$
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1. $f(x) = 2^x$ | $x$ | $f(x)$ | | ---- | ---- | | $-2$ | | | $-1$ | | …
| \( x \) | \( f(x) \) | | ---- | ---- | | \( -2 \) | \( \frac{1}{4} \) | | \( -1 \) | \( \frac{1}{2} \) | | \( 0 \) | \( 1 \) | | \( 1 \) | \( 2 \) | | \( 2 \) | \( 4 \) |
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a point of the form 25 +bi is 37 units from 13 - 31i. what is the value…
4
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ex. 3: given $h(x) = 5x - 1$, find $x$ if $h(x) = 9$
$x = 2$
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evaluating functions ex. 1: given $f(x) = 7x - 1$, find $f(-2)$. ex. 2
$-15$
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for f(x)=4−x and g(x)=3x²+x+9, find the following functions. a. (f∘g)(x…
a. $\boldsymbol{-3x^2 - x - 5}$ b. $\boldsymbol{3x^2 -25x +61}$ c. $\boldsymbol{-19}$ d. $\boldsymbol{23}$
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graph the exponential function. \\( g(x) = -\frac{3}{2}(2)^x \\) plot f…
The five points are \( (-2, -\frac{3}{8}) \), \( (-1, -\frac{3}{4}) \), \( (0, -\frac{3}{2}) \), \( (1, -3) \), \( (2, -6) \). These points can be plotted on the graph to sketch \…
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which function represents exponential growth? a) $y = 8x$ b) $y = 0.5x^…
C) \( y = 3(1.5)^x \)
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graph the exponential function. \\( g(x) = -\frac{3}{2}(2)^x \\) plot f…
The five points to plot are \((-2,-\frac{3}{8})\), \((-1,-\frac{3}{4})\), \((0,-\frac{3}{2})\), \((1, - 3)\), \((2,-6)\) (or in decimal form \((-2,-0.375)\), \((-1,-0.75)\), \((0,…
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multiply and divide fractions (positive) l1 score: 0/3 penalty: none qu…
$\frac{4}{15}$
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determine whether the following graph represents a function. answer fun…
Function
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graph the exponential function. $f(x)=3^x$ plot five points on the grap…
Five points: \((-2, \frac{1}{9})\), \((-1, \frac{1}{3})\), \((0, 1)\), \((1, 3)\), \((2, 9)\). Horizontal asymptote: \( y = 0 \). To graph, plot the points and draw a smooth curve…
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what is the function g(x) created from f(x)=x² by moving the graph righ…
D. $g(x)=\frac{1}{2}(x-3)^2 - 5$
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which statement explains the difference between the graphs of $f(x) = 4…
C. The graph of g(x) is obtained by flipping f(x) over the x-axis and stretching vertically by a factor of 2.
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question 1 of 45 a function, f, is defined by $f(x,y)=3x^2 - 4y$. what …
C. 19
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what is the function ( g(x) ) created from ( f(x) = x^2 ) by moving the…
B. $g(x)=3(x-8)^2 + 6$
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what is the function ( g(x) ) created from ( f(x) = x^2 ) by moving the…
D. $g(x)=\frac{1}{6}(x + 7)^2 - 8$
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question what is the y - intercept of the polynomial $f(x)$ defined bel…
0
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identify both the vertical and horizontal asymptotes of the function. \…
Vertical asymptote: \( x = 2 \); Horizontal asymptote: \( y=-1 \)
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practice & problem solving 15. make sense and persevere let ( f(x) = a^…
19. The graph of $g(x)$ is the graph of $f(x)=2^x$ translated 6 units down. 20. The graph of $p(x)$ is the graph of $f(x)=2^x$ translated 4 units left. 21. The graph of $g(x)$ is …
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identify the horizontal asymptote of the function. $f(x) = -\frac{3}{x …
The horizontal asymptote of the function \( f(x)=-\frac{3}{x + 4}-8 \) is \( y = - 8 \)
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understand 15. make sense and persevere let ( f(x) = a^x ). describe tw…
19. The graph of $g(x)=2^x -6$ is the graph of $f(x)=2^x$ shifted **6 units downward**. 20. The graph of $p(x)=2^{x+4}$ is the graph of $f(x)=2^x$ shifted **4 units to the left**.…
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identify the vertical asymptote of the function.\\( f(x) = \\frac{8}{x …
The vertical asymptote of the function \(f(x)=\frac{8}{x + 2}-2\) is \(x=-2\)
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identify the vertical asymptote of the function. $f(x)=-\frac{7}{x - 2}…
The vertical asymptote of the function \( f(x)=-\frac{7}{x - 2}+7 \) is \( x = 2 \).
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lesson 5 topic review name: period: lesson 5.1 nth root, radicals and r…
The value of \( \sqrt[4]{16^3} \) is \( 8 \)
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50. $f(x)=\\begin{cases}-x + 1&\\text{if }x < -2\\\\5&\\text{if }x\\geq…
1. For $f(x)=\begin{cases}-x + 1 & \text{if } x < -2 \\5 & \text{if } x \geq -2\end{cases}$: - Left segment: Line $y=-x+1$, open at $(-2,3)$, extending left. - Right segment: Hori…
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fill in the symbol that makes the expression true 50 + 120 125 drag the…
>
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29. if $f(x) = x^2$ and $g(x) = f(x + 7.2)$, what is the vertex of the …
$(-7.2, 0)$
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question how many x-intercepts would the function shown below have? $f(…
The function \( f(x)=(x^{2}-5)(x + 5) \) has 3 x - intercepts.
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9. what problem is suggested about shareland’s economy * a. too many ch…
B. Unequal distribution of wealth ### Question 10
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the graph of y = f(x) is shown below. what are all of the real solution…
The real solutions of \( f(x)=0 \) are \( x=-4 \), \( x = 0 \), and \( x = 3 \). So we can write them as \( x=-4,0,3 \) (or list them separately as \( x=-4 \), \( x = 0 \), \( x =…
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49. use the graph to answer the questions below: - what are the x-inter…
1. The x-intercepts are $x=-8$, $x=0$, and $x=8$. 2. For interval $(-8, -4)$: B. it's positive 3. For interval $(2, 6)$: B. it's positive 4. For interval $(-2, 2)$: B. it's positi…
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the graph of $y = f(x)$ is shown below. what are all of the real soluti…
The real solutions of \( f(x) = 0 \) are \( x = -8 \), \( x = -4 \), \( x = 6 \), and \( x = 8 \). So the solutions are \( \boldsymbol{-8, -4, 6, 8} \).
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计算： $\begin{array}{r} 13.67\\ + 0.312\\ hline end{array}$
\(13.982\)
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f(x) = \\begin{cases} -x - 2 & \\text{for} & -6 < x < 2 \\\\ x - 7 & \\…
To graph \( f(x) \): 1. For \( -6 < x < 2 \), graph \( y = -x - 2 \) (open circles at \( (-6, 4) \) and \( (2, -4) \), line connecting them). 2. For \( 2 < x \leq 6 \), graph \( y…
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characteristics of graphs worksheet domain: _________ range: _________ …
Domain: $\boldsymbol{-5 \leq x \leq 5}$ Range: $\boldsymbol{-4 \leq y \leq 4}$ Max: $\boldsymbol{4}$ Min: $\boldsymbol{-4}$ Discrete or continuous? $\boldsymbol{\text{Continuous}}…
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6.3 comparing functions 1. function a is shown by the ordered pairs: (1…
1. a. $y = 3x + 2$ b. 3 2. A. $y = 2x + 2$ B. 2 3. a. B: $m=2$, C: $m=2$ b. Neither function increases faster; they have the same rate of change. 4. a. $y = 1.5x + 6$ b. Both func…
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the graph of y = f(x) is shown below. what are all of the real solution…
The real solutions of \( f(x) = 0 \) are \( x=-8\), \( x=-4\), \( x = 6\), and \( x = 8\).
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Question was provided via image upload.
Exercise 47: a. $f(3)=12$ b. $f(-2)=13$ c. $f(-1)=4$ d. $f(4)=5$ e. $f(5)=5$ Exercise 48: a. $g(-3)=-9$ b. $g(3)=4$ c. $g(-2)=-7$ d. $g(0)=6$ e. $g(4)=4$
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domain: range: max: min: interval of increase: interval of decrease: f(…
Dominio: $[1, 12]$ Rango: $[0, 8]$ Max: $8$ Min: $0$ Interval of increase: $(1, 3)$ Interval of decrease: $(9, 12)$ $f(2)+f(9)=12$
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the graph of y = f(x) is shown below. what are all of the real solution…
The real solutions of \( f(x) = 0 \) are \( x=-6 \), \( x=-4 \), and \( x = 0 \) (or if the graph only crosses at \( x=-6 \) and \( x = 0 \), then \( x=-6 \) and \( x = 0 \); but …
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h(x) = x² + 2x + 3 5. h(-3) to h(0) f(x) = -x² + x - 3 7. f(3) to f(7) …
1. $h(-3)=6$, $h(-2)=3$, $h(-1)=2$, $h(0)=3$ 2. At $x=3$, $y=7$; at $x=1$, $y=1$ 3. $f(3)=-9$, $f(4)=-15$, $f(5)=-23$, $f(6)=-33$, $f(7)=-45$ 4. At $x=5$, $y=8$; at $x=4$, $y=4$
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lets find \\(\\frac{2}{3} - \\frac{1}{4}\\). first write the subtractio…
$\frac{2}{3}-\frac{1}{4}=\frac{8}{12}-\frac{3}{12}=\frac{5}{12}$ (The boxes are filled with 8, 12, 3, 12, 5, 12 respectively)
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the graph of $y = f(x)$ is shown below. what are all of the real soluti…
The real solutions of \( f(x) = 0 \) are \( x = -7 \) and \( x = -3 \). Wait, but the answer box is a single input. Maybe the problem has two solutions, so we need to list them. W…
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find the slope of the line that passes through (4, -10) and (5, 16). si…
26
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2.9 rate of change with equations - day 4 find the average rate of chan…
1. $0$ 2. $1$ 3. $-16$ 4. $1$
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the graph of y = f(x) is shown below. what are all of the real solution…
The real solutions of \( f(x) = 0 \) are the \( x \)-intercepts of the graph. From the graph, the \( x \)-intercepts are at \( x = -5 \), \( x = 0 \), and \( x = 6 \). So the real…
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daily work: jan. 27th graph: ① ( f(x)=\begin{cases}2x - 4 & \text{if } …
1. For $f(x)=2x-4$ where $x>-1$: A ray starting at the open point $(-1, -6)$ with slope 2, extending to the right. 2. For $f(x)=|x+1|$ where $-4<x\leq2$: A V-shaped graph with ver…
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compute. -3.384 - 5.76 = 16.37 + (-29.786) =
$-9.144$ $-13.416$
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the graph of y = f(x) is shown below. what are all of the real solution…
The real solutions of \( f(x) = 0 \) are \( x = -3 \), \( x = 1 \), \( x = 4 \), and \( x = 7 \).
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compute. $-3.46 + (-4.23) = square$ $-7.6 + 39.2 = square$
$-3.46 + (-4.23) = -7.69$ $-7.6 + 39.2 = 31.6$
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for 7 and 8, find the maximum or minimum of the parabola. 7. $y = -2x^2…
The maximum value of the parabola \( y = - 2x^{2}-16x + 20 \) is \( 52 \) (occurring at \( x=-4 \)).
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match the equation with the correct graph\\ $f(x) = -\\frac{3}{2}x + 1$
The correct graph is the bottom one (the line with negative slope passing through $(0,1)$).
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find the average rate of change for each equation. 1. $f(x) = x^2 - 7x …
1. $-3$ 2. $3$ 3. $-2$ 4. $-1$
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3. - food stamp act of 1964 - housing and urban development act of 1965…
the creation of programs to alleviate poverty
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1.c: choose two directions: choose two words that best explain, define,…
1. diaphragm: a. separates, c. divides 2. diameter: b. through, d. circle 3. diagnose: c. identify, d. determine 4. dialect: a. pronunciation, d. grammar 5. permeable: a. absorben…
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find the y-coordinate of the y-intercept of the polynomial function def…
The \(y\) - coordinate of the \(y\) - intercept is \(0\).
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question find the y - coordinate of the y - intercept of the polynomial…
The y - coordinate of the y - intercept is \( 16 \)
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question find the y - coordinate of the y - intercept of the polynomial…
0
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find the y-coordinate of the y-intercept of the polynomial function def…
\(-9\)
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which equation choice could represent the graph shown below? answer $f(…
\(f(x)=(x - 8)(x^{2}-4)\) (the third option, i.e., the option with \(f(x)=(x - 8)(x^{2}-4)\))
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let $f(x) = 3x - 5$. what is $f(4)$? a. 7 b. 9 c. 12 d. 17 #2 * let $g(…
1. A. 7 2. A. 3 3. B. 10
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which equation choice could represent the graph shown below? answer $f(…
\(f(x)=x(x^{2}-36)\)
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which equation choice could represent the graph shown below? answer $f(…
\(f(x)=(x - 3)(x - 7)(x - 7)\)
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which equation choice could represent the graph shown below? answer $f(…
\(f(x)=x(x + 1)(x + 3)\)
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which equation choice could represent the graph shown below? answer $f(…
\(f(x)=(x + 6)(x + 1)(x + 1)\) (the fourth option: \(f(x)=(x + 6)(x + 1)(x + 1)\))
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¿cuál de los siguientes es un principio clave del diseño web? * 2 punto…
1. El diseño web debe priorizar la funcionalidad y la capacidad de respuesta. 2. Publicar entradas de blog periódicamente 3. (Se requieren las opciones completas para responder co…
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which equation choice could represent the graph shown below? answer $f(…
\(f(x)=(x + 7)(x - 5)(x - 2)\) (Option B)
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which equation choice could represent the graph shown below?
To solve this, we analyze the graph's features (degree, roots, leading coefficient, y - intercept) and match with polynomial equations. But since the options aren't provided, we'l…
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7. the graph of a line is represented by the equation ( 5x - 8y = 40 ).…
$\frac{5}{8}$ (corresponding to the second option: $\boldsymbol{\frac{5}{8}}$)
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a quadratic function $f(x)$ is hidden from view. you must find the $y$-…
\((0, -14)\)
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a quadratic function ( f(x) ) is hidden from view. you must find the ( …
To find the \( y \)-intercept of a quadratic function \( f(x) \), we use the **standard form** of a quadratic function, which is \( f(x) = ax^2 + bx + c \), where \( a \), \( b \)…
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a quadratic function f(x) is hidden from view. you must find the maximu…
The maximum value of \( f(x) \) is \( 8 \).
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the study of how people, firms, and governments make decisions about ho…
B. economics
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a quadratic function $f(x)$ is hidden from view. you must find the maxi…
To determine the maximum value of a quadratic function \( f(x) \), the most efficient form to use is the **vertex form** (also known as the standard form for quadratic functions i…
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what is the cube root of 125? \\sqrt3{125} = \\square
\( 5 \)
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a preschool is building a new fenced playground along one side of the b…
Length: 56 m Width: 28 m
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a quadratic function $f(x)$ is hidden from view. you must find the $x$-…
To find the \( x \)-intercepts of a quadratic function \( f(x) \), the most efficient form of the quadratic function to use is the **factored form** (also known as the intercept f…
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a quadratic function $f(x)$ is hidden from view. you must find the $x$-…
\( (3, 0) \) and \( (-1, 0) \)
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a quadratic function $f(x)$ is hidden from view. you must find the $x$-…
To find the \( x \)-intercepts of the quadratic function \( f(x) \) most efficiently, we should select the **factored form** (also known as the intercept form) of the quadratic fu…
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how can reconstruction in south carolina be considered a failure regard…
African American schools received less funding than schools for white students in South Carolina.
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common assessment: back to the basics what is |-93.498|? save answer
93.498
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what is the cube root of 1,000? \\sqrt3{1,000} = an error has occurred.…
10
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c = \\frac{5}{9}(-10)
\( C = -\frac{50}{9} \)
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the formula for the volume of a cube is $v = x^3$, where $x$ is the edg…
64
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which expression has a value of 12? \\(sqrt{24}\\) \\(sqrt{48}\\) \\(sq…
$\sqrt{144}$
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simplify the radical expressions. (answers should be in simplest radica…
7. $\boldsymbol{6\sqrt[4]{135}}$ 8. $\boldsymbol{-6\sqrt[4]{7}}$ 9. $\boldsymbol{5xy^2\sqrt{3x}}$ 10. $\boldsymbol{4x^2y\sqrt[3]{3x}}$ 11. $\boldsymbol{2x\sqrt[5]{3xy^3}}$ 12. $\b…
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the function $g(x)=x^2$ is transformed to obtain function $h$: $h(x)=g(…
B. The graph of h is the graph of g vertically shifted down 5 units.
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4. why does the senate have the power to approve presidential appointme…
4. C. To limit the President's power and prevent unfair appointments 5. C. The Supreme Court strikes down a law that violates the Constitution
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what are the solutions for the system of equations? select all that app…
(1,1), (6,-4)
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what is the largest ( x )-value in solutions for the system of equation…
1
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an artist is painting an amphitheater on a grid canvas. the equations b…
$(0, -3)$ and $(6, -3)$
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can you prove this statement using properties of logarithms? \\log_{7}7…
no
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evaluate the function graphically. find $f(-5)$
\( f(-5)=7 \)
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evaluate the function graphically. find $f(0)$
\( \boldsymbol{-3} \)
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y = -x² + 36 that negative x - values indicate the distance to the left…
Maximum height point: $(0, 36)$ Zero height points: $(-6, 0)$ and $(6, 0)$
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evaluate the function graphically. find ( f(1) )
\(f(1)=6\)
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evaluate the function graphically. find $f(4)$
\( f(4)=-3 \) (Note: There might be a mis - calculation in the initial detailed analysis, but based on the graph's visual representation, the value at \( x = 4 \) is - 3)
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evaluate the function graphically. find $f(1)$
\( f(1)=-1 \)