5.5 Review

Front

What is the composition of functions?

Back

The composition of functions, denoted as (g∘f)(x), means applying function f first and then applying function g to the result. It is defined as g(f(x)).

Front

Given f(x)=2x-8 and g(x)=4x, find g(f(x)).

Back

g(f(x)) = g(2x-8) = 4(2x-8) = 8x - 32.

Front

What does the notation f⋅g represent?

Back

f⋅g represents the product of two functions, defined as (f⋅g)(x) = f(x) * g(x).

Front

Given f(x)=2 and g(x)=-2x+1, find (f⋅g)(x).

Back

(f⋅g)(x) = f(x) * g(x) = 2 * (-2x + 1) = -4x + 2.

Front

How do you evaluate f(g(5)) if f(x)=3x+10 and g(x)=x-2?

Back

First, find g(5): g(5) = 5 - 2 = 3. Then, find f(3): f(3) = 3(3) + 10 = 19.

Front

If f(x)=x^2 and g(x)=3x-1, find g∘f(x).

Back

g∘f(x) = g(f(x)) = g(x^2) = 3(x^2) - 1 = 3x^2 - 1.

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, while a quadratic function has the form f(x) = ax^2 + bx + c.

Front

What is the significance of the slope in a linear function?

Back

The slope (m) indicates the rate of change of the function; it represents how much y changes for a unit change in x.

Front

What does the y-intercept of a function represent?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the value of the function when x=0.