Evaluating functions in functions notation

Front

What is function notation?

Back

Function notation is a way to represent functions using symbols, typically written as f(x), where 'f' is the name of the function and 'x' is the input variable.

Front

How do you evaluate a function at a specific value?

Back

To evaluate a function at a specific value, substitute the value into the function's expression and simplify.

Front

Given h(x) = -2x - 5, what is h(-2)?

Back

h(-2) = -2(-2) - 5 = 4 - 5 = -1.

Front

What does it mean to find 2 ⋅ h(-2)?

Back

It means to multiply the value of h(-2) by 2. If h(-2) = -1, then 2 ⋅ h(-2) = 2 ⋅ (-1) = -2.

Front

Evaluate g(x) = 6ƒ(10) if ƒ(x) = 2x.

Back

ƒ(10) = 2(10) = 20, so g(x) = 6(20) = 120.

Front

What is the result of -1 ⋅ h(1) + 5 if h(x) = -2x - 5?

Back

h(1) = -2(1) - 5 = -2 - 5 = -7, so -1 ⋅ h(1) + 5 = -(-7) + 5 = 7 + 5 = 12.

Front

Given ƒ(x) = 2x, what is ƒ(10)?

Back

ƒ(10) = 2(10) = 20.

Front

Evaluate f(x) = 3x - 4 at x = 2.

Back

f(2) = 3(2) - 4 = 6 - 4 = 2.

Front

What is the general form of a linear function?

Back

A linear function can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a function represent?

Back

The slope represents the rate of change of the function; it indicates how much the output value changes for a unit change in the input value.