Section 1.5 – Analyzing Graphs of Functions
- How to graph a function
- Finding the domain and range of a function from the graph
- Using the Vertical Line Test to determine if a graph represents a function
- Zeros of a function and the \(x\) and \(y\)-intercepts
- Determining the intervals where a function is increasing, decreasing, and constant
- Finding relative maximums and relative minimums of a function
- Definition of even and odd functions
Exercises
Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.
1. Use the graph of the function \(f\) below to find \(f(-1)\), \(f(2)\), and \(f(4)\).
\(f(-1)=3\)
\(f(2)=DNE\)
\(f(4)=DNE\)
The domain of \(f\) is \([-3,2)\), so \(f(2)\) and \(f(4)\) are not defined.
2. Determine whether the function is even, odd, or neither. Then describe the symmetry.
- \(f(x)=x\sqrt[3]{x^4+1}\)
- \(g(x)=\cfrac{x^4-9}{x^2+9}\)
- \(h(x)=x^3-3x^2\)
- Odd
- Even
- Neither