# How to Scale a Function Horizontally?

Horizontal scaling means stretching or shrinking the diagram of function along the $$x$$-axis.  In the following guide, you will learn how to horizontal scaling.

Horizontal scaling refers to the shrinking or stretching of the curve along the $$x$$-axis by some specific units.

## Step by step guide to horizontal scaling

Horizontal scaling means stretching or shrinking the diagram of function along the $$x$$-axis. The horizontal scale can be done by multiplying the input by a constant.

Consider the following example:

If we have a function,$$y=f(x)$$, the horizontal scaling of this function can be written as: $$y=f(Cx)$$.

Note:

• If $$C>1$$, the graph shinks.
• If $$C<1$$, the graph stretches.

The points related to the curves can be related from the following table:

### How is a graph scaled horizontally?

• Steps 1: Select a constant with which we want to scale the function.
• Steps 2: Write the new function as $$g(x)=fC(x)$$, where $$C$$ is the constant.
• Steps 3: Trace the new function graph by replacing each value of $$x$$ with $$Cx$$.
• Steps 4: $$X$$ coordinate of each point in the graph is multiplied by $$±C$$, and the curve shrinks or stretches accordingly.

Let’s understand this with an example:

Suppose we have a quadratic equation $$f(x)=x^2$$ and the graphical representation of the diagram is shown below:

We want to scale this function by a factor of $$+2$$. So the equation of the new function will be:

$$g(x)=2 f(x)=(2x)^2$$

So we have to plot a function:$$f(x)=(2x)^2$$, and it is shrunk by a factor of $$+2$$ units in the $$x$$-direction.

Note: as we have scaled it with a factor of $$+2$$ units, it has made the graph steeper.

### Horizontal Scaling – Example 1:

Horizontally stretch the function $$f(x)=x+2$$ by a factor of $$2$$ units.

## Exercises for Horizontal Scaling

• Horizontal scaling of function $$f(x) = sin x$$ by a factor of $$-3$$.
• Horizontal scaling of function $$f(x) =x^2+3x+2$$ by a factor of $$4$$.

• Horizontal scaling of function $$f(x) = sin x$$ by a factor of $$-3$$.
• Horizontal scaling of function $$f(x) =x^2+3x+2$$ by a factor of $$4$$.

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