Analysis
Grenzwerte, Ableitungen, Optimierung und Funktionsverhalten.
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learn it systems of equations in the last activity, you began exploring…
1. The solution is at the intersection point of the two lines on the graph. 2. Substitute the point's x and y values into each equation in the system. If both equations are satisf…
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on the set of axes below, solve the following system of equations graph…
The solution set is \(\{(-5,2),(-3,-2)\}\) (assuming the second equation is \(y = - 2x-8\) instead of \(y=-2x - 3\) due to the graph's vertex and the need for real intersections)
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6. asymptote: domain: range:
Asymptote: Horizontal asymptote \( y = 0 \), Vertical asymptote \( x=-2 \) Domain: All real numbers \( x > - 2 \) (or \( (-2,\infty) \)) Range: All real numbers \( y > 0 \) (or \(…
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evaluate the integral using any appropri\\(\\int (\\csc x + \\tan x)^2 …
$\tan x - \cot x - x + 2\ln|\sec x + \tan x| + C$ (where $C$ is the constant of integration)
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use the graph of the function ( y = h(x) ) below to answer the question…
(a) No (b) 1 (c) $[-3, 1]$
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7 \\overline{\\$4 9.7 0}
$\$7.10$
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express the function graphed on the axes below as a piecewise function.
\( f(x) = \begin{cases} 2x - 1 & \text{for } -4 \leq x < 3 \\ \frac{2}{3}x + 3 & \text{for } 3 < x \leq 6 \end{cases} \)
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el gráfico de una función ( f ) se muestra a continuación. hallar ( f(-…
\( 0 \)
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on the set of axes below, solve the following system of equations graph…
The solution set is \(\{(4, -3), (9, 2)\}\)
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¿cuál fue un éxito clave del movimiento por el sufragio femenino antes …
La obtención del derecho al voto para las mujeres en algunos estados y territorios del oeste. ### Second Question (Failure/Limitation of Women's Suffrage Movement after 19th Amend…
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express the function graphed on the axes below as a piecewise function.
\( f(x)=\begin{cases}4& \text{for } x < - 1\\x + 3& \text{for } x>3\end{cases} \)
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find the output, y, when the input, x, is 2. y =
$-2$
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which of the following are examples of limited resources in the part of…
time and money
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which of the following has the largest impact on opportunity cost? cons…
limited resources
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456.9 - 58.3= 78 x 125= 67.8 x 2.5=
$456.9 - 58.3 = 398.6$ $78 \times 125 = 9750$ $67.8 \times 2.5 = 169.5$
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the function $y = f(x)$ is graphed below. what is the average rate of c…
$-5$
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alexander hamilton (the federalist party) - believed that mostly the we…
Alexander Hamilton trusted wealthy, elite individuals and a strong central government (the governing elite), as his views prioritize their leadership, strict voting rules to limit…
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research methodology is very important to experimenters but is of limit…
False
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adding mixed numbers with different denominators step 1: find the least…
\(8\frac{5}{6}\) ### Parte b:
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in the selection from frankenstein, what does the creature most hope fo…
C. to gain their friendship ### Second Question (Multiple - Choice)
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analyzing the graph of a linear function consider the graph of the line…
Quadrant II, because the slope is positive and the y-intercept is negative
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a utility company says that the cost of operating a hair dryer is \\(\f…
2
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representing a graph with a slope-intercept equation a function f(x) is…
$y=2x+1$
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assume f is an even function and g is an odd function. assume f and g a…
2
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identify the key features of each rational function. 12. $f(x)=\\frac{-…
Horizontal Asymptote: \( y = -1 \) Vertical Asymptote(s): \( x = -4 \) Holes: None ### Problem 13: \( f(x)=\frac{2x + 6}{x^{2}-9} \)
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use shifts and scalings to transform the graph of $f(x)=\\sqrt{x}$ into…
For the transformation: D. Shift 6 units to the left. For the graph: A.
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evaluate the piecewise function at the given values of the independent …
(a) $h(3)=5$ (b) $h(0)=2$ (c) $h(2)=8$
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use shifts and scalings to transform the graph of $f(x)=\\sqrt{x}$ into…
D. Shift 6 units to the left.
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find an equation for the line below.
The equation of the line is \(y = -\frac{3}{4}x+\frac{11}{4}\) (or equivalent forms like \(3x + 4y=11\))
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evaluate the piecewise function at the given values of the independent …
(a) $f(-2) = -1$ (b) $f(0) = 5$ (c) $f(4) = 9$
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6-21. graph the lines $y = x + 2$ and $y = 2x - 1$ on the same set of a…
\((3, 5)\)
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16 for what value of x is \\(\\cos(x) = \\sin(14^\\circ)\\), where \\(0…
D. $76^\circ$
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writing a linear function choose the answer to complete each statement …
g(x) = (7/3)x - 3
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write an equation:
\( y = 2x + 4 \)
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7 multiple choice 10 points all money which is used in a market must be…
A. Uniform ### Question 8
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3x - 4(2.5) = 10
$x = -\frac{2}{3}$
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graphing an equation in slope-intercept form graph ( y = \frac{3}{4}x +…
(-4, 2)
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graphing an equation in slope-intercept form graph ( y = \frac{3}{4}x +…
### Table of points: | $x$ | $y$ | |-----|-----| | $-4$ | $2$ | | $0$ | $5$ | | $4$ | $8$ | To graph: Plot the points $(-4,2)$, $(0,5)$, and $(4,8)$, then draw a straight line thr…
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graphing an equation in slope-intercept form graph the linear function …
Slope = $-3$, y-intercept = $-2$ To graph: 1. Plot the y-intercept point $(0, -2)$ on the coordinate plane. 2. Use the slope $\frac{-3}{1}$: from $(0, -2)$, move 3 units down and …
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discussion questions - | fun facts about the life of jackson | write a …
### Discussion Questions - Fun Facts About the Life of Jackson | Fun Facts About the Life of Jackson | Write a + for admire & a - for problematic | Words to describe him | |------…
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what did the 1970 revision of the clean air act establish for the criti…
(Assuming the last option, though partially cut, is "ambient air quality standards") The correct option (the last one, likely "ambient air quality standards") as the 1970 Clean Ai…
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day 5 – the end of reconstruction and its impact sol focus: usii.2f not…
The end of Reconstruction, marked by the Compromise of 1877, drastically changed life in the South, especially for African Americans. When federal troops were ordered to withdraw,…
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graph this function. $f(x) = \\begin{cases}\\frac{1}{4}x - 7 & \\text{i…
1. Trazar la recta $f(x)=\frac{1}{4}x-7$ por los puntos $(0, -7)$ y el punto abierto $(4, -6)$, solo para $x<4$. 2. Trazar la recta $f(x)=2x-14$ por el punto cerrado $(4, -6)$ y $…
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the graph of $f(x)=x^2$ is translated to form $g(x)=(x - 5)^2 + 1$. whi…
The graph with vertex at $(5,1)$ opening upward (the option shown in the lower grid with vertex at the point 5 units right and 1 unit up from the origin) is the correct representa…
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12. graph: $y = \\frac{4}{3}x$
The graph of \( y = \frac{4}{3}x \) is a straight line passing through the origin \((0,0)\) and the point \((3,4)\) (and other points satisfying the equation), drawn by plotting t…
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graph this function. $f(x) = \\begin{cases} -x - 4 & \\text{if } x < 4 …
- Para la rama $f(x) = -x - 4$ ($x<4$): puntos graficados incluyen $(0, -4)$ y el punto abierto $(4, -8)$, con una línea que se extiende hacia la izquierda. - Para la rama $f(x) =…
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analyzing a relationship between functions justine graphs the function …
left 13 units, down 2 units
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$y = \\frac{1}{2}x + 4$ $y = -x + 1$ plot two lines by clicking the gra…
$(-2, 3)$
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determining characteristics of a graph consider the graph of the functi…
$(-\infty, -3)$
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graph the function. $y = -\\sqrt{x - 1}$ click to plot points on the gr…
The graph has an endpoint at $(1, 0)$, passes through $(2, -1)$, $(5, -2)$, $(10, -3)$, and is a downward-opening square root curve defined for $x \geq 1$.
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practice with quadratic functions in vertex form. what is the axis of s…
$x=2$ Vertex: $(2, 4)$
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3.) check the boxes that represent exponential functions.
Check the boxes for the second and fifth graphs (the ones with the exponential - growth - like and exponential - decay - like curves respectively).
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determine the domain on which the following function is decreasing.
$(4, 9)$
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determine the domain on which the following function is decreasing.
$(6, 15)$
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1) select 2 different colors to sketch the graphs below $y = 3(2)^{x}$ …
For \( y = 3(2)^x \): | x | y | |----|------| | -2 | 0.75 | | -1 | 1.5 | | 0 | 3 | | 1 | 6 | | 2 | 12 | For \( y = 3(\frac{1}{2})^x \): | x | y | |----|------| | -2 | 12 | | -1 | …
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determine the domain on which the following function is decreasing.
$(-\infty, 1)$
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divide. give the exact answer, written as a decimal. \\(\\begin{array}{…
4225.5
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suppose that the function f is defined, for all real numbers, as follow…
$f(-5)=-\frac{9}{4}$ $f(2)=1$ $f(4)=0$
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find the difference quotient of f, that is, find \\(\\frac{f(x + h) - f…
$2x + h - 2$
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use successive approximations to estimate a solution of this equation: …
Completed table values: $0.5^{-1.15} \approx 2.2$, $2.5(-1.15)^2 -1 \approx 2.3$ Estimated solution: $x \approx -1.2$
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this is the graph of a polynomial function. there is no absolute minimu…
Domain: \((-\infty, \infty)\) Range: \((-\infty, \infty)\)
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post test: exponential and logarithmic functions which statements descr…
- domain of \( \{x \mid -\infty < x < \infty\} \) - horizontal asymptote of \( y = 0 \) - y - intercept at \( (0,4) \)
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which of these were included in the salt i (strategic arms limitation t…
a. a cap on nuclear arms, d. a limit on launch sites
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the graph of a function ( h ) is shown below. use the graph of the func…
2
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6. what is the value of the expression? $64.58 + 7.426 = __________$
$72.006$
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use the graph to determine a. open intervals on which the function is i…
a. A. The function is increasing on the interval(s) $(-\infty, 2)$ b. The function is decreasing on the interval(s) $(2, \infty)$ c. B. There is no interval on which the function …
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graph the equation shown below by transforming the given graph of the p…
The graph of $y=|3x|$ is a horizontally compressed (by factor $\frac{1}{3}$) version of $y=|x|$, with vertex at $(0,0)$, passing through points like $(1,3)$, $(-1,3)$, $(2,6)$, $(…
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find the real - number root using a calculator. round your answer to th…
5.408
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rewrite the logarithmic expression as a single logarithm with the same …
\(\log_{y} e^{12}\) (or \(12\log_{y} e\), but the form as a single logarithm with the argument as a single power of \(e\) is \(\log_{y} e^{12}\))
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use the graph to answer the question. find the interval(s) over which t…
$(-\infty,-3)$
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use transformations of $f(x)=x^2$ to graph the following function.\\ $g…
D. The graph of $f(x)=x^2$ should be shifted 4 units up.
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the function $g(x)$ is graphed below. rewrite the points on the graph i…
## Table: | \( x \) | \( g(x) \) | |--------|-----------| | -4 | 3 | | -3 | 2 | | -1 | 0 | | 2 | -3 | | 4 | -5 | ## Function Notation: \( g(-4) = 3 \), \( g(-3) = 2 \), \( g(-1) =…
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function a and function b are linear functions. function a (graph of a …
The y-value of Function A when x = 1 is greater than the y-value of Function B when x = 1.
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for the following exercise, use a graphing utility to estimate the loca…
Local extrema: (local minimum at $x=9$, $f(9)=-2185$) Increasing on the interval: $(9, \infty)$ Decreasing on the interval: $(-\infty, 9)$
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what is the equation of this linear function? y = ?x +
$y = 4x + 2$
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express the function graphed on the axes below as a piecewise function.
\( f(x) = \begin{cases} x + 5 & \text{if } x \leq -4 \\ -6 & \text{if } x > 0 \end{cases} \)
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find the equation of the line written in point - slope form with the gi…
\(y + 2=3(x - 7)\)
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graph this line using the slope and y-intercept: y = (1/7)x + 9 click t…
1. Plot the point $(0, 9)$ (the y-intercept). 2. Plot the point $(7, 10)$ (found using the slope $\frac{1}{7}$). 3. Draw a straight line passing through these two points to graph …
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5 longdiv 67
The result of \( 67\div5 \) is \( 13.4 \) (or \( 13 \) with a remainder of \( 2 \)).
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resuelve si x = 9. 4x + 27 =
63
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determine the domain on which the following function is decreasing.
$(-\infty, -2)$
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determine the domain on which the following function is increasing
$x > 2$ or in interval notation: $(2, \infty)$
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determine the domain on which the following function is increasing.
$(-\infty, -2)$
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determine the domain on which the following function is decreasing.
$(-\infty, 4)$ or all real numbers less than 4
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mine the domain on which the following function is increasing.
$[0, 6]$
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graph a function where interval (1) is an increasing interval, interval…
The correct graph is the one that satisfies: (1) increasing (rises with \( x \)), (2) decreasing (falls with \( x \)), (3) constant (horizontal), (4) decreasing (falls with \( x \…
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find and simplify the difference quotient \\(\\frac{f(x + h) - f(x)}{h}…
$-4x - 2h - 1$
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analyzing the graph of a quadratic function the function ( f(x) = -0.3(…
- The axis of symmetry is $x = 5$ - The domain is $\{x \mid x \text{ is a real number}\}$ - The function is increasing over $(-\infty, 5)$
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find the difference quotient of f, that is, find \\(\\frac{f(x + h) - f…
$4x+2h-1$
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doug tried to evaluate an expression. here is his work: $65 - 20 \\div …
No, Doug made a mistake going from Step 3 to Step 4. Doug should have divided 20 by 2 before multiplying. The order of operations says to multiply and divide from left to right.
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kiara tried to evaluate an expression. here is her work: $5^3 - 3 + 24 …
Yes, Kiara's work is correct.
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monica tried to evaluate an expression. here is her work: $(7 + 9) - (2…
Yes, Monica's work is correct.
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find the difference quotient of f, that is, find \\(\\frac{f(x + h) - f…
$-8$
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nina tried to evaluate an expression. here is her work: $(5\\cdot 4 - 1…
No, Nina made a mistake going from Step 4 to Step 5. Nina should have divided 16 by 2 before adding. The order of operations says to divide before you add.
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find and simplify the difference quotient \\(\frac{f(x + h) - f(x)}{h}\…
$-7$
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joey tried to evaluate an expression. here is his work: $97 - 3 + 5^3 \…
No, Joey made a mistake going from Step 4 to Step 5. Joey should have subtracted 3 from 97 before adding. The order of operations says to add and subtract from left to right.
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evaluate the piecewise function at the given values of the independent …
a. $g(0)=3$ b. $g(-6)=3$ c. $g(-3)=0$
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graphing a quadratic function in vertex form graph ( h(x) = 0.5(x + 2)^…
$h(-6)=4$ Additionally, completing the table: | $x$ | $y$ | |-----|-----| | $-6$ | $4$ | | $-4$ | $-2$ | | $-2$ | $-4$ | | $0$ | $-2$ | | $2$ | $1$ | The axis of symmetry is $x=-2…
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graphing a quadratic function in vertex form graph ( h(x) = 0.5(x + 2)^…
$-2$
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evaluate the piecewise function at the given values of the independent …
(a) $f(-2) = -6$ (b) $f(0) = 7$ (c) $f(1) = 8$