Evaluating Functions - Algebra I Grade 9

Evaluating Functions

In this lesson, we will learn how to evaluate functions. Evaluating a function involves substituting a value into the function and computing the result. This is a fundamental skill in algebra that helps in understanding how functions work.

Outline

Understanding Function Notation
Substituting Values into Functions
Example Problems
Practice Exercises
Homework
Revision

Examples

Example 1

Given the function f(x) = 2x + 3, find f(4).

Solution: Substitute x = 4 into the function:

f(4) = 2(4) + 3 = 8 + 3 = 11

Example 2

Given the function g(x) = x^2 - 5x + 6, find g(2).

Solution: Substitute x = 2 into the function:

g(2) = 2^2 - 5(2) + 6 = 4 - 10 + 6 = 0

Example 3

Given h(x) = \frac{1}{x + 1}, find h(-2).

Solution: Substitute x = -2 into the function:

h(-2) = \frac{1}{-2 + 1} = \frac{1}{-1} = -1

Example 4

Given f(x) = 3x^2 - 2x + 1, find f(0).

Solution: Substitute x = 0 into the function:

f(0) = 3(0)^2 - 2(0) + 1 = 0 - 0 + 1 = 1

Example 5

Given g(x) = 2x - \frac{3}{x}, find g(1).

Solution: Substitute x = 1 into the function:

g(1) = 2(1) - \frac{3}{1} = 2 - 3 = -1

Example 6

Given h(x) = \sqrt{x + 4}, find h(5).

Solution: Substitute x = 5 into the function:

h(5) = \sqrt{5 + 4} = \sqrt{9} = 3

Exercises

1. Evaluate f(x) = x^3 - 2x for x = -1.

Solution: f(-1) = (-1)^3 - 2(-1) = -1 + 2 = 1

2. Evaluate g(x) = 4x + 7 for x = 3.

Solution: g(3) = 4(3) + 7 = 12 + 7 = 19

3. Evaluate h(x) = \frac{2x}{x - 1} for x = 2.

Solution: h(2) = \frac{2(2)}{2 - 1} = \frac{4}{1} = 4

4. Evaluate f(x) = 5 - x^2 for x = -3.

Solution: f(-3) = 5 - (-3)^2 = 5 - 9 = -4

5. Evaluate g(x) = \sqrt{2x + 3} for x = 4.

Solution: g(4) = \sqrt{2(4) + 3} = \sqrt{8 + 3} = \sqrt{11}

6. Evaluate h(x) = \frac{x^2 - 1}{x + 1} for x = 0.

Solution: h(0) = \frac{0^2 - 1}{0 + 1} = \frac{-1}{1} = -1

Homework

1. Evaluate f(x) = 2x^2 - 3x + 4 for x = 5.

2. Evaluate g(x) = \frac{3x + 2}{x - 4} for x = 6.

3. Evaluate h(x) = \sqrt{x^2 + 1} for x = -2.

4. Evaluate f(x) = x^3 - 4x for x = 1.

5. Evaluate g(x) = 7 - \frac{x}{2} for x = 8.

6. Evaluate h(x) = \frac{x + 1}{x - 2} for x = 3.

Revision

To review what we have learned about evaluating functions:

Function notation represents a function as f(x), where x is the input variable.


                To evaluate a function, substitute the given value into the function and simplify.
                Be careful with different types of functions such as linear, quadratic, and rational functions when substituting values.
                Practice various functions to strengthen your understanding of how to handle different function types and operations.



        Video Explanation
        Watch the following video for a comprehensive explanation of evaluating functions:
        

        For more help, contact us for tutoring or text our numbers to book a tutor. Follow us on Facebook and YouTube for more educational content.

        Return to the Algebra I Menu.