Finding Inputs and Outputs of Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x), where x is the input.

Front

How do you find the output of a function?

Back

To find the output of a function, substitute the input value into the function's equation and simplify.

Front

What does f(x) = x + 1 represent?

Back

This is a linear function where the output is one more than the input.

Front

Calculate f(-1/5) for f(x) = x + 1.

Back

f(-1/5) = -1/5 + 1 = 4/5 or 0.8.

Front

What is the slope of the function f(x) = 3x + 2?

Back

The slope is 3, indicating that for every 1 unit increase in x, f(x) increases by 3 units.

Front

Find f(-2) for f(x) = 3x + 2.

Back

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

Front

What does the absolute value function do?

Back

The absolute value function, denoted as |x|, returns the non-negative value of x.

Front

Calculate f(1) for f(x) = -|x + 5| + 6.

Back

f(1) = -|1 + 5| + 6 = -6 + 6 = 0.

Front

What is the equation of a line in slope-intercept form?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

Find x when f(x) = -3/4 for f(x) = 3x + 6.

Back

Set 3x + 6 = -3/4. Solve for x: 3x = -3/4 - 6; x = -9/4 or -2.25.