Q: Given the graph in Image 1, which of the following is the correct piecewise-defined function for $$f(x)$$?

$$f(x) = \begin{cases} -x-1 & x \u003c -2 \\ x^2$-5 & -2 \leq x \u003c 2 \\ 3 & x \geq 2 \end{cases}$$

Q: Given the graph in Image 2, which of the following is the correct piecewise-defined function for $$g(x)$$?

$$g(x) = \begin{cases} -(x+3)^2$+7 & x \u003c -2 \\ x^2$-5 & x \geq -2 \end{cases}$$

Question 1

Given the graph in Image 1, which of the following is the correct piecewise-defined function for $$f(x)$$?

Accepted Answer

$$f(x) = \begin{cases} -x-1 & x \u003c -2 \ x^2$-5 & -2 \leq x \u003c 2 \ 3 & x \geq 2 \end{cases}$$

Question 2

For the function $$f(x) = \begin{cases} -x-1 & x \u003c -2 \ x^2$-5 & -2 \leq x \u003c 2 \ 3 & x \geq 2 \end{cases}$$, what is the value of $$f(-2)$$?

Accepted Answer

Question 3

Given the graph in Image 2, which of the following is the correct piecewise-defined function for $$g(x)$$?

Accepted Answer

$$g(x) = \begin{cases} -(x+3)^2$+7 & x \u003c -2 \ x^2$-5 & x \geq -2 \end{cases}$$

Question 4

Which of the following best describes the transformation from $$y = x^2$ to y$$ = $$(x-2)^2 + 3$?

Accepted Answer

Shift right 2 units and up 3 units

Question 5

Given the function $$f(x) = 2x^2$ - 8x + 3$$, find the vertex of the parabola.

Accepted Answer

$$(2, -5)$$

Question 6

Which of the following is the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 7

Find the average rate of change of $$f(x) = x^2$ between x = 1$ and x = 4$.

Accepted Answer

$$5$$

Question 8

Which of the following is the correct equation for a parabola that opens downward, is reflected across the $$x-$$axis, shifted left 3 units, and up 2 units?

Accepted Answer

$$y = -(x+3)^2$ + 2$$

Question 9

Given the polynomial $$f(x) = x^4$ - 5x^2$ + 4$$, which of the following is a zero of the function?

Accepted Answer

$$x = 1$$ and $$x = -1$$

Question 10

Which of the following is the correct application of the Laws of Logarithms to expand $$\log_b(xy^2$)$$?

Accepted Answer

$$\log_b x + 2\log_b y$$

Question 11

Solve for $$x$$: $$2^x = 16.$$

Accepted Answer

$$x = 4$$

Question 12

If the population of a city grows exponentially at a rate of 2% per year, how long will it take for the population to double?

Accepted Answer

$$t = \frac{\ln 2}{0.02}$$

Question 13

Which of the following is the solution to the system of equations: $$\begin{cases} x + y = 5 \ x - y = 1 \end{cases}$$?

Accepted Answer

$$(3, 2)$$

Question 14

Given $$f(x) = \frac{x^2$-4}{x-2}$$, what is the vertical asymptote?

Accepted Answer

$$x = 2$$

Question 15

Which of the following is the correct single logarithm for $$\log_b x + \log_b y$$?

Accepted Answer

$$\log_b(xy)$$

Question 16

If $$f(x) = x^3$ - 3x^2$ + 2x$$, which of the following is a zero of $$f(x)$$?

Accepted Answer

$$x = 1$$

Question 17

Which of the following is the correct solution for $$\log_2$(x) = 3$$?

Accepted Answer

$$x = 8$$

Piecewise Functions: Writing Equations from Graphs

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