Question 1

Given the graph in Image 1, what is the x-intercept of the function?

Accepted Answer

$$x = -1$$

Question 2

Given the function $$f(x) = -0.65x + 1375.5$$ representing the decline in stock value, what does the slope represent in this context?

Accepted Answer

The average decrease in stock value per year

Question 3

For the function $$f(x) = x - 7$$, on which interval is $$f$$ increasing?

Accepted Answer

$$(-\infty, \infty)$$

Question 4

Given the graph in Image 2, what is the y-intercept of the function?

Accepted Answer

$$y = 1$$

Question 5

Calculate the average rate of change of $$f(x) = 2x + 1$$ from $$x_1 = 1$ to x_2$ = 3.$$

Accepted Answer

$$2$$

Question 6

Find the difference quotient for $$f(x) = 4x - 8$$ and simplify.

Accepted Answer

$$4$$

Question 7

Solve the quadratic equation $$x(x - 4) = -40$$ and write the solutions in standard form.

Accepted Answer

$$x = 2 \pm 2\sqrt{11}$$

Question 8

Given the temperature data: 8:00 am = 82°F, 11:00 am = 95°F, what is the average rate of change in temperature between these times?

Accepted Answer

$$4.33$$ degrees/hour

Question 9

Given the graph in Image 4 for $$f(x) = x^2$ - 6x + 8$$, how many real zeros does the function have?

Accepted Answer

2

Question 10

Given the graph in Image 5, estimate the absolute maximum of the function.

Accepted Answer

$$y \approx 4.5$$

Question 11

Given the graph in Image 6, estimate the local minimum value of the function.

Accepted Answer

$$y \approx -4$$

Question 12

Determine whether the function $$f(x) = 2x^2$ - 1 is $$even, odd, or neither.

Accepted Answer

Even

Question 13

If $$f is an $$even function and $$f(-8) = 5$$, $$f(-4) = 2$$, what is $$f(8)$$?

Accepted Answer

$$5$$

Question 14

A rock is thrown vertically upward from the surface of the moon. Based on the graph in Image 8, what does the turning point represent?

Accepted Answer

The point at which the rock reaches its maximum height and starts to fall back towards the surface of the moon.

Question 15

State the end behavior of $$f(x) = x^2$ + x^3$ + 4.$$

Accepted Answer

Down on left side, up on right side

Question 16

Evaluate $$f(0)$$ for $$f(x) = \begin{cases} x - 8, & x \u003c 2 \ 3 - x, & x \geq 2 \end{cases}.$$

Accepted Answer

$$-8$$

Question 17

Divide $$4x^3$$ + $$6x^2 - 6x - 4$ by x + 2$ using long division. What is the remainder?

Accepted Answer

$$-20$$

Question 18

Given the graph in Image 9, estimate the x-intercepts and determine the minimum degree of $$f.$$

Accepted Answer

$$-4, 1, 2; 4$$

Question 19

For the piecewise function $$f(x) = \begin{cases} x + 2, & x \u003e 0 \ 4, & x \leq 0 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$4$$

Question 20

Solve the quadratic equation $$x^2 + 35 = 5x$ and write the solutions in standard form.

Accepted Answer

$$x = \frac{5 \pm \sqrt{(-5)^2$ - 4 \cdot 1 \cdot 35}}{2}$$

Precalculus Unit 1 Review: Step-by-Step Study Guidance

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