Evaluating Linear Functions

Front

What is 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.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the value of the function when x = 0. It is the point where the graph of the function crosses the y-axis.

Front

How do you evaluate a linear function at a specific point?

Back

To evaluate a linear function at a specific point, substitute the value of x into the function and calculate the corresponding value of f(x).

Front

If f(x) = 3x + 2, what is f(1)?

Back

f(1) = 3(1) + 2 = 5.

Front

What is the process to find the x-value when given f(x)?

Back

To find the x-value when given f(x), set the function equal to the desired output and solve for x.

Front

If f(x) = 2x + 1, what value of x makes f(x) = 7?

Back

Set 2x + 1 = 7. Solving gives x = 3.

Front

What does it mean for a function to be undefined at a certain point?

Back

A function is undefined at a certain point if there is no output for that input, often due to division by zero or taking the square root of a negative number.

Front

Evaluate f(-3) if f(x) = -x + 4.

Back

f(-3) = -(-3) + 4 = 3 + 4 = 7.

Front

What is the value of g(2) if g(x) = 5x - 3?

Back

g(2) = 5(2) - 3 = 10 - 3 = 7.