Evaluating Functions

Front

What is the definition of a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set, known as the domain.

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 formula to find the corresponding output value.

Front

How do you evaluate the function f(x) = x^2 - 5x at x = -4?

Back

Substitute -4 into the function: f(-4) = (-4)^2 - 5(-4) = 16 + 20 = 36.

Front

What is the output of the function f(x) = 4x + 5 when x = 4?

Back

Substituting 4 into the function gives f(4) = 4(4) + 5 = 16 + 5 = 21.

Front

How do you find f(-5) for the function f(x) = 3x^2 - 11?

Back

Substitute -5 into the function: f(-5) = 3(-5)^2 - 11 = 3(25) - 11 = 75 - 11 = 64.

Front

What is the value of f(-5) for the function f(x) = x + 3?

Back

Substituting -5 into the function gives f(-5) = -5 + 3 = -2.

Front

How do you evaluate the function f(x) = 2x + 2 for x = 4?

Back

Substituting 4 into the function gives f(4) = 2(4) + 2 = 8 + 2 = 10.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the slope in a linear function?

Back

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

Front

What is the y-intercept in a linear function?

Back

The y-intercept (b) is the value of the function when the input (x) is zero; it is the point where the graph intersects the y-axis.