Composite Functions and Function Rules

The video tutorial explains how to evaluate composite functions using given values, graphs, and function rules. It covers three examples: calculating f(g(x)) for x = -1, f(g(x+1)) for x = 1, and h(f(x) + g(x)) for x = 4. Each example involves finding the inner function value and then using it to determine the outer function value, utilizing tables and graphs for reference.

What are the three types of data provided to solve the composite function problem?

• A table for f(x), a graph for g(x), and a function rule for h(x)

• A graph for f(x), a table for g(x), and a function rule for h(x)

• A table for f(x), a function rule for g(x), and a graph for h(x)

• A function rule for f(x), a graph for g(x), and a table for h(x)

When x = -1, what is the value of g(x) according to the graph?

• 0

• -1

• 2

• 1

What is the value of f(1) based on the table?

• -2

• 2

• 0

• 1

For x = 1, what is the value of g(x+1) according to the graph?

• 1

• -1

• 0

• 2

What is the value of f(-1) based on the table?

• 0

• -3

• 3

• 1

When x = 4, what is the value of f(x) according to the table?

• 1

• 0

• -3

• 3

For x = 4, what is the value of g(x) according to the graph?

• 0

• 2

• 1

• -1

What is the function rule for h(x)?

• x^2 + 3

• x^2 - 3

• x^2 + 1

• x^2 - 1

What is the value of h(4) using the function rule?

• 14

• 15

• 12

• 13

What is the final composite function value for h(f(x) + g(x)) when x = 4?

• 13

• 15

• 12

• 14