# Algebra Sample Problems

1. Add/subtract fractions

**Example:**

**Answer:**

2. Absolute Value

**Examples**

b. Solve the equation for x.

(Answer: x= -4, x=7)

3. Exponents

**Examples**

4. Factor a quadratic equation

**Example:** Factor the following expression.

**Answer :**

5. Simplify a radical function

**Example:** Simplify the following expression.

**Answer :**

6. Simplify a complex fraction.

**Example: **Simplify.

**Answer :**

7. Simplify radical expressions.

**Example:** Simplify.

**Answer :**

8. Given an equation, solve for x.

**Examples**

9. Solve an inequality

**Example: **Solve the inequality and write the solution set in interval
notation.

Graph the solution set.

10. Find coordinates of a point

**Example:** Find the coordinates of the point C.

11. Read data from graph.

**Example:** Suppose the following graph represents sales of DVD players (in

dollars) for Locke Industries in 2007.

a. What was the sales amount on June 1? (Answer: $3500.
00)

b. What was the maximum sales amount? (Answer: $4500. 00)

c. In what month did the maximum sales occur? (Answer: August)

d. In what months was sales equal to $3000. 00?

(Answer: April, November, December)

12. Find x and y intercepts.

Example: Find the x-and y-intercepts of the graph of the equation

Answer: x-intercept is (12,0), y-intercept is (0,-4)

13. Lines

**Examples**

a. Find the slope of the line.

b. Find the equation of the line that passes through the points (4,-1) and (-6,14).

**Answer:**

14. Domain and range of a function.

**Example:** Find the domain and range of

**Answer:**

domain is [-7,∞], range is [0,∞]

15. Graph a function by making a table of values and plotting points.

16. Find values of a function by looking at a graph.

**Example:** Given below is the graph of y=g(x) .

a. What is the value of g(2)?

**Answer: -5**

b. What are the values of x such that g(x)=0?

**Answer:-3. 5, 3. 1**

17. Function Values

**Example:** If f(x)=2x+8 what is the value of f(z+2)?

**Answer:**2z+12

18. Composition of functions

Example: If f(x)=x^2 and g(x)=x+4, what is ?

**Answer:**