Evaluating Functions

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean to evaluate a function?

Back

To evaluate a function means to calculate the output of the function for a given input value.

Front

How do you find the value of x when f(x) = k?

Back

To find the value of x when f(x) = k, set the function equal to k and solve for x.

Front

What is the significance of the x-intercept in a function?

Back

The x-intercept is the point where the function crosses the x-axis, indicating the value of x when f(x) = 0.

Front

What is the process to solve a linear equation like w(x) = mx + b?

Back

To solve a linear equation, isolate x by rearranging the equation to get x on one side and the constants on the other.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the roots of a quadratic equation ax² + bx + c = 0.

Front

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

Back

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

Front

What does it mean for a function to have multiple outputs for a single input?

Back

A function cannot have multiple outputs for a single input; if it does, it is not a function.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, while a quadratic function has the form f(x) = ax² + bx + c.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing if its output values rise as the input values increase, and decreasing if the output values fall as the input values increase.