How to Find the Y-Intercept of a Function

Finding the Y-Intercept of a Function

The y-intercept of a function is found where the graph of a function crosses the y-axis on a pair of Cartesian coordinate axes.

How to Find the Y-intercept of a Function

The y-intercept of a function f(x) is found by evaluating the function at x = 0.

This uses functional notation (see Note) to express the following idea.

The y-intercept is the value of the function at the y-axis. Along the y-axis, the value of x is 0. The input x of the function equals 0.

The image below shows what we mean:

A Real Example of How to Find the Y-intercept of a Function

Finding the y-intercept of a function is easy.

Question

What is the y-intercept of the function f(x) = 2x − 3?

Step-by-Step:

1

Write the function. This is a linear equation.

f(x) = 2x − 3

Note: 2x = 2 × x.

2

Substitute x = 0 into the function.

f(0) = 2 × 0 − 3

f(0) = 0 − 3

f(0) = −3

Answer:

The y-intercept of f(x) = 2x − 3 is −3.

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The slider below shows another real example of how to find the y-intercept of a function.

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Another Real Example of How to Find the Y-intercept of a Function

Question

What is the y-intercept of the function f(x) = x2 + 4x + 2?

Step-by-Step:

1

Write the function. This is a quadratic equation.

f(x) = x2 + 4x + 2

Note: x2 = x × x (x squared) and 4x = 4 × x.

2

Substitute x = 0 into the function.

f(0) = 02 + 4 × 0 + 2

f(0) = 0 × 0 + 4 × 0 + 2

f(0) = 0 + 0 + 2

f(0) = 2

Answer:

The y-intercept of f(x) = x2 + 4x + 2 is 2.

See Also

What is a function? Evaluating a function What is a linear equation? What is a quadratic equation?