# Graphing Parent functions

Graphing parent functions such as quadratic, cubic, log and exponential functions.

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#### Solution Preview

This lesson shows how to graph the parent functions of quadratic, cubic, log and exponential. See attachment for graphs.

Graphing Parent Functions

Description: Graphing parent functions of quadratic, cubic, log and exponential functions.

Quadratic Function

Example 1

Graph y = x2.

Solution

Step 1: Identify the domain and range of the function.

Domain = R, the set of all real numbers, that is, (-∞,∞).

So the graph exists for all values of x.

Since x2 is non-negative for all values of x, the range is the set of all non-negative real numbers. That is, the graph exists only for non-negative values of y. So the graph doesn't exist below the x-axis.

Step 2: Find the intercepts.

For x-intercept, put y = 0.

0 = x2.

From this, x = 0.

For y-intercept, put x = 0.

y = 0.

So the graph passes through the origin (0, 0).

Step 3: Find the asymptotes.

No asymptote occurs for the graph.

Step 4: Determine the symmetry of the graph.

Here, f(x) = x2.

f(-x) = (-x)2 = x2 = f(x)

So the graph is symmetric ...

#### Solution Summary

This solution gives detailed steps in graphing y = x^2, y = x^2, y = log (x) and y = e^X.