Question 1

Which of the following is the solution set to the equation $$\sqrt{2x+15} - 6 = x + 6$$?

Accepted Answer

$$\{3\}$$

Question 2

Given $$|1 - \frac{3}{x}| = \frac{7}{4}$$, which of the following is a valid solution for $$x$$?

Accepted Answer

$$x = 3$$

Question 3

Is $$y a $$function of $$x$$ for the equation $$y^3 = 27 - x$?

Accepted Answer

Yes, because for each $$x$$ there is exactly one real $$y$$ value.

Question 4

For the equation $$x = 4y^2$ + 16$$, is $$y a $$function of $$x$$?

Accepted Answer

No, because for some $$x$$ there are two possible $$y$$ values.

Question 5

Given $$f(x) = -9x + 4$$, what is $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$-9$$

Question 6

Given $$g(x) = 7 - x^2$, what is $$\frac{g(x+h) - g(x)}{h}$$?

Accepted Answer

$$-2x - h$$

Question 7

Determine whether the function $$f(x) = x^3$ - 5 is $$even, odd, or neither.

Accepted Answer

Neither even nor odd

Question 8

Which of the following functions is even?

Accepted Answer

$$g(x) = x^8$ + 7x^2$

Question 9

Given $$h(x) = x^7$ - x^3$, what is h(-x$$)$$?

Accepted Answer

$$-x^7$$ + $$x^3$$

Question 10

Given the function $$f(x) = 2x^2$ - 7$$, what is the value of $$f(-2)$$?

Accepted Answer

$$1$$

Question 11

For the function $$f(x) = 2x^2$ - 7$$, what is the $$x-$$value where the function switches from negative to positive values?

Accepted Answer

$$x = -2$$

Question 12

Which of the following best describes the symmetry of $$g(x) = x^8$ + 7x^2$?

Accepted Answer

Even symmetry (symmetric about the $$y-$$axis)

Question 13

If $$f(x) = x^3$ - 5$$, what is $$f(-x)$$?

Accepted Answer

$$-x^3 - 5$

Question 14

Given the function $$f(x) = 2x^2$ - 7$$, which of the following $$x-$$values yields $$f(x) = 9$$?

Accepted Answer

$$x = 3$$

Question 15

Which of the following statements is true about the function $$h(x) = x^7$ - x^3$?

Accepted Answer

It is an odd function.

Question 16

If $$f(x) = 2x^2$ - 7$$, what is the range of $$f(x)$$?

Accepted Answer

$$[-7, \infty)$$

Question 17

Given $$f(x) = x^3$ - 5$$, what is the degree of the function?

Accepted Answer

$$3$$

Question 18

Which of the following best describes the end behavior of $$f(x) = x^3$ - 5 as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o \infty$$

Question 19

If $$g(x) = 7 - x^2$, for which x$-value does g(x) = 0$?

Accepted Answer

$$x = \pm \sqrt{7}$$

Question 20

Suppose a function $$f is $$defined as $$f(x) = 2x^2$ - 7. $$Which of the following statements is true?

Accepted Answer

The function is even because $$f(-x) = f(x)$$ for all $$x.$$

Functions, Equations, and Symmetry in College Algebra

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