Q: If $$f(x) = x^2$ - 4x + 4$$, what is the end behavior of the function?

As $$x \to \infty$$, $$f(x) \to \infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Question 1

What is the slope of the line passing through the points $$(-7, -2)$$ and $$(4, 3)$$?

Accepted Answer

$$\frac{5}{11}$$

Question 2

Find the equation of the line containing the point $$(5, -1)$$ and perpendicular to the line $$y = 2x + 1.$$

Accepted Answer

$$y = -\frac{1}{2}x + \frac{3}{2}$$

Question 3

What is the domain of the function $$f(x) = \frac{2}{x^2$ - 5}$$?

Accepted Answer

$$x 
eq \pm \sqrt{5}$$

Question 4

Find the domain of the function $$f(x) = \log_2${(2x + 3)}.$$

Accepted Answer

$$x \u003e -\frac{3}{2}$$

Question 5

Find the domain of the function $$f(x) = \sqrt{x^2$ - 4}.$$

Accepted Answer

$$x \leq -2 or$$ $$x \geq 2$$

Question 6

Given $$f(x) = x^2$ + x - 2$$ and $$g(x) = x + 5$$, find $$f(g(0)).$$

Accepted Answer

$$28$$

Question 7

For the function $$f(x) = x^2$ - 2x + 4$$, use the difference quotient $$\frac{f(x+h) - f(x)}{h} to $$find the simplified expression.

Accepted Answer

$$2x + h - 2$$

Question 8

Which of the following describes the horizontal asymptote of $$f(x) = \frac{x^2$ - x - 2}{2x^2$ + x - 1}$$?

Accepted Answer

$$y = \frac{1}{2}$$

Question 9

Given the quadratic function $$f(x) = -x^2$ + 4x - 3$$, what is the maximum value?

Accepted Answer

$$1$$

Question 10

If $$f(x) = x^2$ - 4x + 4$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 2$$

Question 11

Find the remaining zeros of $$f(x) = x^3$ + 4x^2$ + x - 6$$ given that $$1 is a $$zero.

Accepted Answer

$$x = -3, x = -2$$

Question 12

Convert the exponential equation $$4^x = 21$$ into a logarithmic equation.

Accepted Answer

$$x = \log_4${21}$$

Question 13

Solve for $$x$$: $$3^x = 411.$$

Accepted Answer

$$x = \log_3${411}$$

Question 14

Charley puts $$2500 in a $$savings account that compounds interest quarterly at $$4.75\%. $$How much money will he have in his account after $$7$$ years? Use $$A = P\left(1 + \frac{r}{n}\$$right)^{nt}$$.

Accepted Answer

$$A = 2500\left(1 + \frac{0.0475}{4}\$$right)^{28}$$

Question 15

Given $$f(x) = \sqrt{x - 2}$$ and $$g(x) = x^2$ - 1$$, find $$g(f(x))$$ and its domain.

Accepted Answer

$$g(f(x)) = x - 3$$, domain: $$x \geq 2$$

Question 16

Solve the system of equations: $$3x - 2y = 8$$ and $$5x + y = 23.$$

Accepted Answer

$$x = 3, y = 4$$

Question 17

What is the horizontal asymptote of $$f(x) = \frac{x^4$ + 4x^2$}{x^4$ + 1}$$?

Accepted Answer

$$y = 1$$

Question 18

Given $$f(x) = x^2$(x - 3)^2$(x - 1)$$, what is the degree of the polynomial?

Accepted Answer

$$5$$

Question 19

If $$f(x) = x^2$ - 4x + 4$$, what is the end behavior of the function?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o \infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 20

Which transformation is applied to $$f(x) = \frac{1}{5^x} to $$obtain $$f(x) = \frac{1}{5^x} - 3$$?

Accepted Answer

A downward shift by 3 units

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