Question 1

Which of the following is the correct domain of the function $$f(x) = \sqrt{x-3}$$?

Accepted Answer

$$[3, \infty)$$

Question 2

Find all values of $$x$$ satisfying the following conditions: $$y = \frac{x^2$}{2}$$, $$y = x + 2$$, and $$y = -1$$, $$y = 1.$$

Accepted Answer

$$x = -2$$

Question 3

Simplify and write in the form $$a + bi$$: $$\frac{6}{1 - 2i}$$

Accepted Answer

$$\frac{6}{1 - 2i} = \frac{6 + 12i}{5}$$

Question 4

Solve the quadratic equation $$2x^2 - 3x + 4 = 0$. Which of the following is a solution?

Accepted Answer

Question 5

Find the sum of the solutions to the quadratic equation $$2x^2 - 10x = 50$.

Accepted Answer

$$10$$

Question 6

Given $$f(x) = x^2$ - 7x + 43$$ and $$g(x) = 2x^2$ + 7x + 53$$, find $$g(x) - f(x).$$

Accepted Answer

$$g(x) - f(x) = 2x^2$ + 7x + 53 - (x^2$ - 7x + 43) = x^2$ + 14x + 10$$

Question 7

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$ - 7x$$

Question 8

Find the inverse of $$f(x) = \frac{2x - 3}{4}.$$

Accepted Answer

$$f^{-1}(x$$) = \frac{4x + 3}{2}$$

Question 9

How can the graph $$y = 2|x - 4| - 5 be $$obtained from the graph $$y = |x|$$?

Accepted Answer

Stretched by factor 2 then shifted right 4 units and down 5 units.

Question 10

Find the equation of the line containing the point $$(2, -3)$$ and parallel to the line $$2x - y = 5.$$

Accepted Answer

$$y = 2x - 7$$

Question 11

If $$f(x) = x^2$ + 2x + 3$$ and $$g(x) = x^2$ - 3x + 5$$, find $$f(x) + g(x).$$

Accepted Answer

$$2x^2 - x + 8$

Question 12

Find the solution of the equation $$9 - \sqrt{2x - 3} = 5x.$$

Accepted Answer

$$x = 6$$

Question 13

Given $$f(x) = x^2$ - 7x + 43$$, find $$f(-7).$$

Accepted Answer

$$172$$

Question 14

For $$f(x) = 2x^2$ + x + 1$$ and $$g(x) = x - 1$$, find $$f(g(2)).$$

Accepted Answer

$$9$$

Question 15

Find the equation of the line passing through $$(2,5)$$ and $$(-4,3).$$

Accepted Answer

$$y = \frac{1}{3}x + \frac{17}{3}$$

Question 16

Find all values of $$x$$ satisfying the following conditions: $$y = 2x$$, $$x = 2y$$, and $$y + y = 1.$$

Accepted Answer

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

Question 17

Find the sum of the solutions to the equation $$x^2 - 10x + 9 = 0$.

Accepted Answer

$$10$$

Question 18

Which of the following is the correct solution to $$\sqrt{9 - 2x} = \sqrt{2x - 3}$$?

Accepted Answer

$$x = 6$$

Question 19

Find the equation of the line containing the point $$(2, -3)$$ and parallel to the line $$2x - y = 5.$$

Accepted Answer

$$y = 2x - 7$$

College Algebra: Practice Questions and Key Concepts

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