Question 1

Evaluate the function $$F(x) = x^2$ - 4x - 7 at$$ $$x = -3.$$

Accepted Answer

$$14$$

Question 2

Given the function $$F(x) = x^2$ - 4x - 7$$, what is $$F(x+h)$$?

Accepted Answer

$$x^2 + 2xh$$ + $$h^2 - 4x - 4h - 7$

Question 3

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-1}$$?

Accepted Answer

$$[1, \infty)$$

Question 4

A function $$f(x) is $$said to be even if:

Accepted Answer

$$f(-x) = f(x)$$

Question 5

Given the piecewise function $$f(x) = \begin{cases} x+6 & x \u003c -2 \ x-6 & x \geq -2 \end{cases}$$, what is the range of $$f(x)$$?

Accepted Answer

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

Question 6

Find the average rate of change of the function $$f(x) = x^2$ - 3x$$ from $$x = -2 to$$ $$x = 5.$$

Accepted Answer

$$4$$

Question 7

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$ - x$$

Question 8

Given $$f(x) = x^2$ - 4x - 7$$, what is the simplified form of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h - 4$$

Question 9

Which of the following intervals describes where the function $$f(x) is $$increasing, given the graph of a downward-opening parabola with vertex at $$(2, 0)$$?

Accepted Answer

$$(-\infty, 2)$$

Question 10

A real-world application: The height $$h (in $$meters) of a ball thrown upward from a building is given by $$h(t) = -5t^2$ + 20t + 50. $$What is the average rate of change of height from $$t = 1 to$$ $$t = 3$$ seconds?

Accepted Answer

$$-15 m/s$$

Question 11

Given $$f(x) = x^2$ - 4x - 7$$ and $$g(x) = x - 1$$, find $$(f \circ g)(2).$$

Accepted Answer

$$-10$$

Question 12

Which of the following is the equation of a line in slope-intercept form that passes through $$(2,4)$$ and has a slope of $$-3$$?

Accepted Answer

$$y = -3x + 10$$

Question 13

Find the inverse of the function $$f(x) = x^2$ - 5$$ for $$x \geq 0.$$

Accepted Answer

$$f^{-1}(x$$) = \sqrt{x+5}$$

Question 14

Given $$f(x) = \frac{1}{x-2}$$, what is the domain of $$f in $$interval notation?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 15

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$ - 3$$, what is $$(f + g)(x)$$?

Accepted Answer

$$x^2 + 2x - 2$

Question 16

Which of the following best describes the $$y-$$intercept of the line $$3x - 4y = 8$$?

Accepted Answer

$$(0, -2)$$

Question 17

Given $$f(x) = x^2$ - 4x - 7$$, what is the value of $$x$$ for which $$f(x) = 3$$?

Accepted Answer

$$x = 5 or$$ $$x = -1$$

Question 18

Which of the following is the equation of a line in slope-intercept form that is perpendicular to $$4x - 2y = 8$$ and passes through $$(0, 5)$$?

Accepted Answer

$$y = \frac{1}{2}x + 5$$

Question 19

If $$f(x) = x^2$ - 4x - 7$$, what is the $$x-$$intercept(s) of the function?

Accepted Answer

$$(2 + \sqrt{11}, 0)$$ and $$(2 - \sqrt{11}, 0)$$

Functions and Graphs: College Algebra Chapter 1 Review

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