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..jpg)
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.
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.
A Note on Notation
For a function, the input is often denoted by x and the function by f(x), which is equal to the output.
By choosing an input x, the function gives an output.
To find the y-intercept, the input x = 0.
The function f(x) becomes f(0).
The notation is the same for any value of x, whether a number or symbol:
The key point is that x is a variable. It can take many values. The function tells you how to relate that input to an output.
When a certain value of x is substituted in, a certain output comes out.
Evaluating a Function
Evaluating a function means putting an input into a function, and finding the output it relates to. When a value is chosen for the input x, the output can be found by substituting that value in for x wherever it is found in the function. For example, if the function is:
f(x) = x + 1
Evaluating the function at x = 0 means substituting 0 for x wherever it is found in the function.
f(0) = 0 + 1
f(0) = 1
This page was written by Stephen Clarke.
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