Graphing parent functions such as quadratic, cubic, log and exponential functions.© BrainMass Inc. brainmass.com October 2, 2020, 5:45 am ad1c9bdddf
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.
Graph y = x2.
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 ...
This solution gives detailed steps in graphing y = x^2, y = x^2, y = log (x) and y = e^X.