2A Composition of Functions and Operations

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs.

Front

What does it mean to compose functions?

Back

Composing functions means applying one function to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).

Front

How do you find h(g(x)) if h(x) = -4x + 3 and g(x) = 4x - 2?

Back

First, find g(x) for a specific x, then substitute that result into h(x). For example, g(6) = 4(6) - 2 = 22, then h(22) = -4(22) + 3 = -85.

Front

What is the formula for g(a) = 4a + 1?

Back

This is a linear function where the slope is 4 and the y-intercept is 1.

Front

How do you evaluate g(h(1)) if g(a) = 4a + 1 and h(a) = -3a + 2?

Back

First, calculate h(1) = -3(1) + 2 = -1, then substitute into g: g(-1) = 4(-1) + 1 = -3.

Front

What is the value of g(5) + h(-2) if g(a) = 4a + 1 and h(a) = -3a + 2?

Back

Calculate g(5) = 4(5) + 1 = 21 and h(-2) = -3(-2) + 2 = 8. Thus, g(5) + h(-2) = 21 + 8 = 29.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, characterized by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, indicating the output value when the input is zero.

Front

How do you determine the x-value for which f(x) = -2?

Back

Set the function equal to -2 and solve for x. For example, if f(x) = 2x + 3, set 2x + 3 = -2 and solve for x.

Front

What is the difference between independent and dependent variables in a function?

Back

The independent variable is the input of the function (usually x), while the dependent variable is the output (usually y) that depends on the input.