Function Notation and Evaluating Functions

Front

What is function notation?

Back

Function notation is a way to represent a function using symbols, typically in the form f(x), where f denotes the function and x is the input variable.

Front

How do you convert an equation into function notation?

Back

To convert an equation like y = 2x - 3 into function notation, you write it as f(x) = 2x - 3.

Front

What does it mean to evaluate a function?

Back

Evaluating a function means substituting a specific value for the variable in the function and calculating the result.

Front

How do you evaluate h(x) = -x^2 + 3x at x = 5?

Back

To evaluate h(5), substitute 5 into the function: h(5) = -5^2 + 3(5) = -25 + 15 = -10.

Front

What is the result of evaluating f(-2) if f(x) = x^2 + 3?

Back

To evaluate f(-2), substitute -2 into the function: f(-2) = (-2)^2 + 3 = 4 + 3 = 7.

Front

What is the value of f(0) for the function f(x) = -3x + 3?

Back

To find f(0), substitute 0 into the function: f(0) = -3(0) + 3 = 0 + 3 = 3.

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 y changes for a unit change in x.

Front

What does the y-intercept represent in a function?

Back

The y-intercept (b) is the value of the function when x = 0; it is the point where the graph intersects the y-axis.

Front

How do you find the value of a function at a specific point?

Back

To find the value of a function at a specific point, substitute the x-value into the function and simplify.