Question 1

Given the correspondence shown in the first image, is this relation a function? Justify your answer.

Accepted Answer

No, because the element 6 in the domain is paired with more than one element in the range.

Question 2

Given the correspondence shown in the second image, is this relation a function? Justify your answer.

Accepted Answer

Yes, because each element in the domain is paired with exactly one element in the range.

Question 3

Which of the following best describes the graph on the left in the third image?

Accepted Answer

It is the graph of a function because every vertical line intersects the graph at most once.

Question 4

Which of the following best describes the graph on the right in the third image?

Accepted Answer

It is not the graph of a function because some vertical lines intersect the graph more than once.

Question 5

For the function $$f(x) = x^2$ - 2x + 1$$, what is the domain?

Accepted Answer

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

Question 6

Find the domain of $$g(x) = \frac{7}{5-x}.$$

Accepted Answer

$$(-\infty, 5) \cup (5, \infty)$$

Question 7

Given $$f(x) = x^2$ - 3$$, find $$f(2a). $$

Accepted Answer

$$4a^2 - 3$

Question 8

Given $$f(x) = x^2$ - 3$$, find $$f(a+h) - f(a). $$

Accepted Answer

$$2ah + h^2$

Question 9

Solve the system using substitution: $$\begin{cases} 2x - 3y = 7 \ 3x - y = 1 \end{cases}$$

Accepted Answer

$$x = 2, y = 1$$

Question 10

Multiply the polynomials: $$(2x^3$$ - $$3x^2 + x$$ + $$5)(2x^2 + x - 1$$)$$

Accepted Answer

$$4x^5$$ - $$4x^4$$ + $$2x^3$$ + $$7x^2 + 4x - 5$

Question 11

Factor completely: $$x^2 - 10x + 25$

Accepted Answer

$$(x - 5)^2$

Question 12

Perform the operation and simplify: $$\frac{y^2$ - 10y + 25}{y^2$ - 1} \cdot \frac{y + 4}{y^2$ - 5y - 3}$$

Accepted Answer

$$\frac{(y - 5)^2$(y + 4)}{(y - 1)(y + 1)(y^2$ - 5y - 3)}$$

Question 13

Divide using long division: $$(6x^3$$ - $$x^2 - 10$$) \div (3x + 4)$$

Accepted Answer

$$2x^2$$ - \frac{3}{2}x + 2 - \frac{18}{3x + 4}$$

Question 14

The sum of two numbers is 9. Two times the larger number plus three times the smaller number is 2. What are the numbers?

Accepted Answer

The numbers are $$-5$$ and $$14.$$

Question 15

Two angles are supplementary. Their difference is $$22^\circ. $$What are the angles?

Accepted Answer

$$101^\circ$$ and $$79^\circ$$

Question 16

For the graph of $$f in $$the fourth image, what is $$f(4)$$?

Accepted Answer

$$3$$

Question 17

For the graph of $$f in $$the fourth image, what is the domain?

Accepted Answer

$$[-3, 5]$$

Question 18

For the graph of $$f in $$the fourth image, for which $$x-$$values is $$f(x) = -1$$?

Accepted Answer

$$x = -1$$ and $$x = 3$$

Question 19

For the graph of $$f in $$the fourth image, what is the range?

Accepted Answer

$$[-2, 3]$$

College Algebra Review: Functions, Graphs, Domain, and Range

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