What is the domain and range of m(x)=5x2+9??

1 Answer
Jul 24, 2018

Domain - all reals x
Range - 0<y59

Explanation:

Looking at the graph, you can immediately tell that it is an even function and and the graph is positive

Even function is when f(x)=f(x)
f(x)=5x2+9
f(x)=5(x)2+9=5x2+9=f(x)
Therefore, 5x2+9 is an even function

It is positive because x2+9 is always positive for all real integers

We also know that there is no x-intercept but there is a y-intercept at (0,59)

Drawing the graph, we can see that:
Domain - all reals x
Range - 0<y59

For the range, y0 because the graph is approaching the asymptote y=0 so it will never touch the line y=0

The graph is below
graph{5/(x^2+9) [-10, 10, -5, 5]}