Question 1

Given the relation $$\{(10, -3), (5, -7), (-6, 9), (-6, -4)\}$$, what is the domain and range?

Accepted Answer

domain = \{-6, 10, 5\}; range = \{9, -3, -7, -4\}

Question 2

Determine whether the relation $$\{(-8, -6), (-8, 7), (1, -3), (3, -4), (8, 1)\} is a $$function.

Accepted Answer

Not a function

Question 3

Does the equation $$x + y^2$ = 4$$ define $$y as a $$function of $$x$$?

Accepted Answer

y is not a function of x

Question 4

Evaluate $$f(x) = -3x + 7 at$$ $$x = 4.$$

Accepted Answer

$$-5$$

Question 5

Given $$f(x) = x^2$ + 4$$, find and simplify $$f(x + 4).$$

Accepted Answer

$$x^2 + 8x + 20$

Question 6

Use the vertical line test to determine if the graph in $$image_3 is a $$function.

Accepted Answer

Function

Question 7

Use the graph in $$image_4 to $$determine the interval where the function is increasing.

Accepted Answer

$$(-2, 2)$$

Question 8

For $$f(x) = x^3$ - 3x^2$ + 1$$, use the graph in $$image_6 to $$find any relative maxima and minima.

Accepted Answer

maximum: $$(0, 1)$$; minimum: $$(2, -3)$$

Question 9

Determine whether $$f(x) = x^3$ - 2x is $$even, odd, or neither.

Accepted Answer

Odd

Question 10

Evaluate the piecewise function $$f(x) = \begin{cases} -3x - 2 & x \u003c 2 \ 4x - 5 & x \geq 2 \end{cases} at$$ $$x = 5.$$

Accepted Answer

$$15$$

Question 11

Find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ for $$f(x) = 4x - 3$$, $$h 
eq 0.$$

Accepted Answer

$$4$$

Question 12

Find the slope of the line passing through $$(-9, 8)$$ and $$(6, -6).$$

Accepted Answer

$$-\frac{14}{15}$$

Question 13

Write the equation of the line in point-slope form with slope $$3$$ passing through $$(8, 4).$$

Accepted Answer

$$y - 4 = 3(x - 8)$$

Question 14

Which graph (from images 8-11) represents the equation $$x = 5$$?

Accepted Answer

$$image_11$$

Question 15

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

Accepted Answer

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

Question 16

Given $$f(x) = 2x^2$ - 9x$$ and $$g(x) = x^2$ - 3x - 54$$, find $$\frac{f(x)}{g(x)}.$$

Accepted Answer

$$\frac{2x^2$ - 9x}{x^2$ - 3x - 54}$$

Question 17

Find the inverse of the function $$f(x) = \frac{5}{3x - 4}.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{5}{3x + 4}$$

Question 18

Given $$f(x) = x$$ and $$g(x) = 1/x$$, which function is the inverse of $$h(x) = x^2$?

Accepted Answer

f(x) and h(x)

Question 19

A chemical reaction's rate $$R is $$modeled by $$R(t) = 2t^2$ - 9t$$ and the temperature $$T by$$ $$T(t) = t^2$ - 3t - 54. $$What is the expression for the ratio of rate to temperature as a function of $$t$$?

Accepted Answer

$$\frac{2t^2$ - 9t}{t^2$ - 3t - 54}$$

Graphing the Equation x = 5 in the Rectangular Coordinate System

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