Evaluating Function Types and Compositions

The video tutorial by Hamid L. covers the composition of functions using a given graph. It explains how to evaluate expressions like f(g(-1)), g(f(1)), g(f(-3)), g(f(4)), and g(f(-2)) by identifying the values of the functions f(x) and g(x) at specific points. The tutorial emphasizes understanding the range and domain of the functions and provides step-by-step solutions for each expression.

What is the main focus of the practice test introduced in the video?

• Solving quadratic equations

• Evaluating composition of functions using a graph

• Finding the derivative of a function

• Solving linear equations

What is the function type of f(x) as described in the video?

• Linear function

• Quadratic function

• Exponential function

• Absolute function

What is the function type of g(x) as described in the video?

• Absolute function

• Linear function

• Quadratic function

• Exponential function

In the first example, what is the value of g(-1) on the graph?

• 4

• 5

• 3

• 2

What is the final value of f(g(-1)) in the first example?

• 4

• 3

• 2

• 0

What is the first step in evaluating a composition of functions?

• Find the derivative

• Evaluate the inside function

• Graph the function

• Solve for x

What is the second step in evaluating a composition of functions?

• Solve for x

• Find the derivative

• Evaluate the outside function

• Graph the function

In the second example, what is the value of f(1) on the graph?

• 0

• 2

• 1

• 3

What is the final value of g(f(1)) in the second example?

• 1

• 0

• 3

• 2

In the third example, what is the value of f(-3) on the graph?

• 2

• 3

• 1

• 4