Identifying Functions and Evaluating Functions on a Graph

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

How can you identify a function from a set of ordered pairs?

Back

A relation is a function if no two ordered pairs have the same first element (x-value).

Front

What does it mean to evaluate a function at a specific point?

Back

Evaluating a function at a specific point means substituting the input value into the function's equation to find the corresponding output value.

Front

Evaluate g(2) if g(x) = 3x - 6.

Back

g(2) = 3(2) - 6 = 0.

Front

What is the value of f(5) if f(x) = 4x?

Back

f(5) = 4(5) = 20.

Front

Given f(x) = -x + 2, evaluate f(-5).

Back

f(-5) = -(-5) + 2 = 5 + 2 = 7.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, the curve is not a function.

Front

Is the relation {(1, 2), (2, 3), (1, 4)} a function?

Back

No, it is not a function because the input 1 corresponds to two different outputs (2 and 4).

Front

Evaluate g(-5) if g(x) = x^2 - 4.

Back

g(-5) = (-5)^2 - 4 = 25 - 4 = 21.

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.