Introduction to Functions

Understand what functions are and how to represent them

Introduction to Functions

What is a Function?

A function is a relationship where each input has exactly one output.

Example: $y = 2x + 3$

For each value of $x$ , there's exactly one value of $y$ .

Function Notation

$f(x) = 2x + 3$

Read as: "f of x equals 2x plus 3"

Example: Find $f(4)$ $f(4) = 2(4) + 3 = 11$

Four Ways to Represent Functions

1. Equation

$f(x) = 2x + 1$

2. Table

| x | y | |---|---| | 0 | 1 | | 1 | 3 | | 2 | 5 |

3. Graph

A line or curve on a coordinate plane

4. Words

"The output is one more than twice the input"

Is It a Function?

Vertical Line Test: If a vertical line touches the graph at more than one point, it's NOT a function.

📚 Practice Problems

1Problem 1easy

❓ Question:

If $f(x) = 3x - 2$ , find $f(5)$ .

💡 Show Solution

Solution:

Substitute $x = 5$ into the function: $f(5) = 3(5) - 2$ $f(5) = 15 - 2$ $f(5) = 13$

Answer: $f(5) = 13$

2Problem 2medium

❓ Question:

If $g(x) = x^2 + 4$ , find $g(-3)$ .

💡 Show Solution

Solution:

Substitute $x = -3$ : $g(-3) = (-3)^2 + 4$ $g(-3) = 9 + 4$ $g(-3) = 13$

Answer: $g(-3) = 13$

3Problem 3hard

❓ Question:

A function is defined by $h(x) = 2x + 5$ . For what value of $x$ is $h(x) = 17$ ?

💡 Show Solution

Solution:

Set the function equal to 17: $2x + 5 = 17$

Solve: $2x = 12$ $x = 6$

Check: $h(6) = 2(6) + 5 = 17$ ✓

Answer: $x = 6$

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