Flashcard 3.2 Function Notation and Evaluating Functions (S)

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one corresponding y-value.

Front

What does it mean for a relation to NOT be a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

Evaluate the function f(x) = x² - 8 at x = 2.

Back

f(2) = 2² - 8 = 4 - 8 = -4.

Front

Evaluate the function f(x) = x² - 8 at x = 3.

Back

f(3) = 3² - 8 = 9 - 8 = 1.

Front

What is the sum of f(2) and f(3) for f(x) = x² - 8?

Back

f(2) + f(3) = -4 + 1 = -3.

Front

How do you solve for x in the equation f(x) = 2x + 9 when f(x) = 15?

Back

Set 2x + 9 = 15, then solve for x: 2x = 15 - 9, 2x = 6, x = 3.

Front

Evaluate the function h(n) = n² + 2n at n = 4.

Back

h(4) = 4² + 2(4) = 16 + 8 = 24.

Front

What is the general form of a linear function?

Back

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

Front

How do you determine the slope of a linear function from an equation?

Back

The slope (m) is the coefficient of x in the equation y = mx + b.

Front

What is the y-intercept in the equation y = 1/2x + 2?

Back

The y-intercept is 2, which is the value of y when x = 0.