微積分
極限、導関数、最適化、関数挙動。
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6. classify each function as increasing, decreasing, or constant. expla…
a. \( f(x) = -\frac{2}{3}x \) is a decreasing function. b. \( f(x) = -2.5 \) is a constant function. c. \( f(x) = 3^x \) is an increasing function.
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the functions f and g are defined as follows. f(x) = -5x - 3, g(x) = -2…
\( f(5)= -28 \) \( g(-4)= 125 \)
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solución de ecuaciones exponenciales de varios pas resolver: $7 + 42 \\…
\(a = 3\) (la opción "a = 3")
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the functions f and g are defined as follows. f(x) = 3x - 3 g(x) = 2x³ …
\( f(-7) = -24 \) \( g(-4) = -126 \)
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the functions f and g are defined as follows. f(x)=4x+2 g(x)=2x² -3x fi…
\( f(-6) = -22 \) \( g(-4) = 44 \)
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solución de ecuaciones exponenciales de varios paso resolver: \\(\\frac…
x = 1 (corresponding to the option "x = 1")
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which points lie on the graph of the function $f(x)=\\lceil x \ ceil + …
$(-1.1, 1)$, $(-0.9, 2)$, $(2.2, 5)$
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light travels $3 \\times 10^5$ kilometers in one second. how far does i…
\( 2.01\times 10^{6}\)
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5. determine whether each relationship represents a function or not a f…
s: a. Function, because the vertical line test is satisfied (each vertical line intersects the graph at most once). b. Function, because each x - value has exactly one y - value. …
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at which x-values are the output values of the floor function $g(x) = \…
-8, 0 (the checkboxes for -8 and 0 should be selected)
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evaluate the floor function f(x) = \\lfloor x \ floor for the given inp…
\( f(2) = \boldsymbol{2} \), \( f(6.8) = \boldsymbol{6} \), \( f(-3.3) = \boldsymbol{-4} \)
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compare the functions $f(x) = 50x^2$ and $g(x) = 4^x$ by completing par…
(for part a table): | \( x \) | \( f(x)=50x^2 \) | \( g(x)=4^x \) | |--------|-----------------|---------------| | 3 | 450 | 64 | | 4 | 800 | 256 | | 5 | 1250 | 1024 | | 6 | 1800 …
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evaluate the step function for the given input values. \\( g(x) = \\beg…
\( g(2) = 3 \) \( g(-2) = -4 \) \( g(5) = 5 \)
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determining the domain and range of a step function a step function is …
Domain: real numbers greater than or equal to \(-3\) Range: equal to \(-4\), \(2\), and \(3\)
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function f, graphed below, is not an invertible function. to which inte…
To determine the intervals where we can restrict the domain of \( f \) to make it invertible, we use the **Horizontal Line Test**: a function is invertible (has an inverse) if and…
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a tablet originally costs $299.99. if it is on sale for $249.99, how mu…
The discount is $50.00.
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evaluating a piecewise function using the graph a linear piecewise func…
When \( x=-5 \), \( y = \boldsymbol{3}\); when \( x=-1 \), \( y=\boldsymbol{-2}\); when \( x = 3 \), \( y=\boldsymbol{-4}\)
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test prep audra has a sheet of construction paper that is 23 centimeter…
152
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part a does he need the same number of square inches of glass for each …
Para la segunda ecuación, si suponemos que la otra dimensión es 10, entonces \( 6 \times \boxed{10} = \boxed{60} \) square inches. (Nota: Esto depende del contexto, pero como ejem…
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what is the domain of the step function f(x) = ⌈2x⌉ - 1? ○ {x| x ≥ -1} …
\(\{x| x \text{ is a real number}\}\)
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the graph represents f(x) = ⌊x⌋ + 3. what is f(-2.2)? -2 0 1 2
0
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all points of the step function f(x) are graphed. what is the domain of…
\(\{x|-4 < x\leq4\}\)
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determine the slope of the line shown in the graph. write the slope as …
\(-1\)
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determine the slope of the line shown in the graph. write the slope as …
\(-1\)
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the step function f(x) is graphed. what is the value of f(0)? -2 -1 0 1
-2 (corresponding to the option with - 2, i.e., the first option: \(\boldsymbol{-2}\))
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the lead of a screw is the distance that the screw advances in a straig…
20
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the graph represents $y = \\lceil x \ ceil + 1$. what is $f(-2.75)$? \\…
-2
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improper fractions questions convert the mixed numbers into improper fr…
s (for each problem in order): 1. \( \frac{16}{3} \) 2. \( \frac{22}{5} \) 3. \( \frac{13}{2} \) 4. \( \frac{31}{4} \) 5. \( \frac{38}{6} \) (or \( \frac{19}{3} \)) 6. \( \frac{59…
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the equation y = 3x + 12 represents the total cost, y, of x hot dogs an…
To graph the equation \( y = 3x + 12 \) (assuming the original equation has a typo and should be \( y = 3x + 12 \) instead of \( y = 1x + 12 \) for a more meaningful cost context,…
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the step function f(x) is graphed. what is the value of f(-1)? options:…
-1 (corresponding to the option: -1)
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multiply: 8.2 × 24.8 2.0366 2033.6 203.36 203.46
203.36
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a piecewise function g(x) is represented by the graph. which functions …
B. \( g(x) = -2, x < -2 \), E. \( g(x)=\frac{x}{2}+1,-2\leq x < 1 \), D. \( g(x)=-2x + 6, x\geq1 \) (Note: Using the option labels as per the original: the options are: 1. \( g(x)…
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the graph of the piecewise function f(x) is shown. what is the range of…
\(\{y \mid -5 \leq y \leq -1\}\) (the fourth option)
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write an equation in point slope form given the points (3, 9) and (1, 6)
\( y - 9=\frac{3}{2}(x - 3) \) or \( y - 6=\frac{3}{2}(x - 1) \)
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a piecewise function is defined as shown. $f(x) = \\begin{cases} -x, & …
4
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the piecewise function h(x) is shown on the graph. what is the value of…
0
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write an equation in point slope form to represent this graph. $y - y_1…
\( y - 1 = -2(x - 0) \) (or other valid point - slope form equations using points on the line, e.g., \( y - 0=-2(x - 0.5) \), but using the y - intercept \((0,1)\) and slope \(-2\…
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a coordinate on the graph of $f(x) = \\sqrt3{x}$ is $(64, 4)$. the func…
\(\frac{1}{2}\) (corresponding to the option "A. \(\frac{1}{2}\)" assuming the first option is labeled as such)
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a piecewise function f(x) is defined as shown. $f(x) = \\begin{cases} -…
# Explanation: ## Step1: Analyze the first piece ($0 \leq x < 40$) The function is $f(x) = -\frac{5}{4}x + 90$. Let's check the first table: - For $x = 0$: $f(0) = -\frac{5}{4}(0)…
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which of the following cubic functions has a point of inflection of (6,…
\(y = 2(x - 6)^3 - 8\) (the fourth option)
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the function d(t) defines a traveler’s distance from home, in miles, as…
At 2 hours, the traveler is 725 miles from home. At 3 hours, the distance is constant, at 875 miles. The total distance from home after 6 hours is 1,062.5 miles.
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the piecewise function h(x) is shown on the graph. what is the value of…
-1 (corresponding to the option: -1)
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graph the parabola. ( y = -x^2 ) plot five points on the parabola: the …
Vertex: \((0, 0)\), Left points: \((-1, -1)\), \((-2, -4)\), Right points: \((1, -1)\), \((2, -4)\) (These points can be plotted to graph the parabola \( y = -x^2 \))
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what is the inverse of the function $f(x) = \\frac{1}{9}x + 2$? $\\bigc…
\( h(x)=9x - 18 \) (corresponding to the option \( h(x) = 9x-18 \))
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what is the inverse of the function $f(x) = 2x + 1$? $\\circ\\ h(x) = \…
A. \( h(x)=\frac{1}{2}x-\frac{1}{2} \)
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what is the inverse of the function f(x) = 2x - 10? ○ h(x) = 2x - 5 ○ h…
To find the inverse of the function \( f(x) = 2x - 10 \), we follow these steps: ### Step 1: Replace \( f(x) \) with \( y \) Start by rewriting the function as: \( y = 2x - 10 \) …
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what is ironic about the pigs activities in this excerpt? they had prev…
B. They prohibited alcohol when they took control of the farm
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one sentence that illustrates this playful approach is reset \i long to…
If particular care and attention is not paid to the Ladies we are determined to foment a Rebellion...
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69) $x - \frac{7}{3+x}$ 70) $\frac{x^2 - 5}{x^2 + 5x - 14} - \frac{x + …
No solution (since \(x = 2\) is extraneous)
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if f(x) = 6x - 4, what is f(x) when x = 8? ○ 2 ○ 16 ○ 44 ○ 52
44
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which function represents a vertical stretch by a factor of 1.85 with a…
\( \boldsymbol{r(x) = 1.85\sqrt{3(x + 2)}-1} \) (the option corresponding to \( r(x) = 1.85\sqrt{3(x + 2)}-1 \))
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what are the zeros of the function $f(x) = x^2 + 5x + 5$ written in sim…
\( x = \frac{-5 \pm \sqrt{5}}{2} \) (corresponding to the option \( x = \frac{-5 \pm \sqrt{5}}{2} \))
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select all the correct answers. which two concepts do both of these let…
- the claim that in reality, women dominate men - the idea that women, children, and apprentices are all becoming rebellious (Or if the correct options are different, but based on…
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which of the following functions is one-to-one? (1 point) - ( f(x) = -6…
\(f(x)=-6x^{3}+7\) (the first option: \(f(x)=-6x^{3}+7\))
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y = 2x - 2 x\ty \t-2 \t0 \t2 \t4
When \( y=-2 \), \( x = 0 \); when \( y = 0 \), \( x=1 \); when \( y = 2 \), \( x = 2 \); when \( y = 4 \), \( x=3 \) So the completed table (filling in the \( x \) values) is: | …
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question determine the value of y, if x is 144. $y = \\sqrt{x} + 11$
23
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question determine the value of y, if x is 81. ( y = sqrt{x} + 9 ) answ…
18
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question determine the value of y, if x is 4. ( y = sqrt{x} - 1 ) answe…
1
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question determine the value of y, if x is 1. ( y = sqrt{x} + 4 )
\( y = 5 \)
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question determine the value of y, if x is 144. ( y = sqrt{x} - 3 )
\( y = 9 \)
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heather is writing a quadratic function that represents a parabola that…
\(f(x)=-x^{2}-12x - 36\) (the fourth option)
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50. a writer who is interested in others sharing, changing, and even bu…
C. attribution share - alike
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add: 2.134 + 345.04 366.174 366.838 347.174 347.178
347.174 (the bottom - left option: 347.174)
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for the functions $f(x)=\\sqrt{x - 4}$ and $g(x)=5x$ find the following…
\(5\sqrt{x - 4}\)
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for the functions $f(x) = \\sqrt{x - 4}$ and $g(x) = 5x$ find the follo…
\(\sqrt{5x - 4}\)
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for the functions $f(x) = \\sqrt{x - 2}$ and $g(x) = 3x$ find the follo…
\(\sqrt{3x - 2}\)
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add no common denominator $\frac{5}{15} + \frac{1}{3} = $
\(\frac{2}{3}\)
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find the sum: \\(\\frac{2}{18} + \\frac{1}{3} = \\frac{\\square}{\\squa…
$\frac{4}{9}$
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\\(\\frac{12}{30} + \\frac{1}{5} = \\frac{\\quad}{\\quad}\\) hint: you …
\(\frac{3}{5}\)
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$\\frac{19}{42} + \\frac{1}{6} = \\frac{\\square}{\\square}$
$\frac{13}{21}$
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subtract: 167.12 − 47.32 120.2 119.4 119.8 120.8
119.8
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which represents the solution(s) of the system of equations, $y = -x^2 …
(3, 25) and (7, 9)
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subtract: 7.86 - 4.501 3.35 3.359 3.369 3.361
3.359 (corresponding to the option "3.359")
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number - fractions - add unlike mixed numbers find the sum. simplify yo…
\(6\frac{5}{8}\)
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number - fractions - add unlike mixed numbers find the sum. simplify yo…
\(9\frac{8}{9}\)
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which represents the solution(s) of the graphed system of equations, $y…
The solutions are \((-2, -3)\) and \((1, 0)\)
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find the sum. simplify your answer. 3\\frac{5}{10} + 1\\frac{1}{5} = \\…
\( 4\frac{7}{10} \)
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algebra 2a semester online practice complete this assessment to review …
A. \((9, 10)\)
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find the sum. simplify your answer. $4 \\frac{7}{8} + 4 \\frac{2}{4} = …
\( 9\frac{3}{8} \) (or in the boxed form as per the problem's layout, the whole number part is 9, numerator is 3, denominator is 8)
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find the least common multiple (lcm) of 3 and 8.
8
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calculate: \\(\\frac{13}{20} - \\frac{2}{5} = \\frac{\\square}{\\square…
$\frac{1}{4}$
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add: 34.05 + 9.068 43.038 43.118 33.018 42.218
43.118 (which corresponds to the option "43.118" among the given choices)
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which statement accurately describes how adding a number, n, to the fun…
There is a vertical shift of \( n \) units.
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what is the range of exponential function g?
The range of the exponential function \( g \) is all real numbers greater than \( - 2 \), or in interval notation \( (-2,\infty) \)
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graph the function. g(x) = \\frac{1}{3}(x - 6)^2 + 1
To graph \( g(x)=\frac{1}{3}(x - 6)^3+1 \): 1. Start with the parent cubic \( y=\frac{1}{3}x^3 \) (inflection at \((0,0)\), increasing, smooth curve). 2. Shift the graph 6 units r…
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type the correct answer in each box. use numerals instead of words. if …
The values to fill in the blanks (from left to right, top to bottom for the empty boxes) are \( \frac{3}{8} \) (or \( 0.375 \)), \( 3 \), \( 1 \), \( -21 \) respectively. If we co…
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lim_{x\\to\\infty} \\frac{e^{3x} + 4}{e^{2x} - e^x}
\(\infty\) (or we can say the limit does not exist (diverges to infinity))
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calculate: \\frac{14}{15} - \\frac{1}{5} = \\frac{\\square}{\\square}
\(\frac{11}{15}\)
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graph the function. \\( g(x) = -\\frac{3}{2}\\left(x - \\frac{5}{2}\ ig…
To graph \(g(x)=-\frac{3}{2}(x - 2)^2\): 1. **Vertex**: \((2,0)\) (from vertex form \(y = a(x - h)^2+k\), \(h = 2\), \(k = 0\)). 2. **Direction**: Opens downward (due to \(a=-\fra…
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which of the following is true for f(x) = -2sin(x) - 3? the range of th…
The amplitude of the function is 2. (The option stating "The amplitude of the function is 2.")
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vertical compression of \\(\\frac{1}{2}\\), horizontal stretch to a per…
vertical compression of \(\frac{1}{2}\), horizontal stretch to a period of \(4\pi\), vertical shift of 1 unit up, phase shift of \(\pi\) units left
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which transformations are needed to change the parent sine function to …
A. vertical compression of \(\frac{1}{2}\), horizontal stretch to a period of \(4\pi\), vertical shift of 1 unit up, phase shift of \(\pi\) units left (assuming the first option i…
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answer attempt 2 out of 2 $f(x) = \\begin{cases} -2x - 4 & \\text{for }…
The piece - wise function \(f(x)=\begin{cases}-2x - 4&\text{for }-5 < x\leq0\\\frac{5}{2}x-8&\text{for }0 < x\leq6\end{cases}\) correctly represents the given graph.
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solve the following logarithmic equation. use a calculator if appropria…
A. \(x = 1\)
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answer attempt 1 out of 2 $f(x) = \\begin{cases} \\square \\text{ for }…
\( f(x)=\begin{cases}-2x - 4& \text{for }-5<x\leq0\\\frac{5}{2}x-8& \text{for }0<x\leq6\end{cases} \)
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find the domain of the function $f(x)=\\frac{3x - 8}{x + 8}$. write bot…
Set - builder notation: B. The domain of \( f \) is \( \{x|x\text{ is a real number and }x eq - 8\} \) Interval notation: \( (-\infty,-8)\cup(-8,\infty) \)
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evaluate the function f(x) = -6x + 5 at the indicated values. a) find f…
a) \( f(0)=\boldsymbol{5} \) b) \( f(-7)=\boldsymbol{47} \)
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express the function graphed on the axes below as a piecewise function.…
\(f(x)=\begin{cases}\frac{9}{2}x + 11& \text{for }-4<x<-2\\\frac{5}{6}x+\frac{17}{3}& \text{for }-2<x<4\end{cases}\)
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express the function graphed on the axes below as a piecewise function.…
\(f(x)=\begin{cases}4 & \text{for } x < 2\\-x + 8 & \text{for } x>5\end{cases}\)
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e function graphed on the axes below as a piecewise functio attempt 2 o…
The piecewise function is \( f(x)=\begin{cases}4, & x < 2\\-x + 8, & 2 < x < 5\end{cases} \)