U3 Math Review: Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x), where x is the input.

Front

What is the formula for the area of a circle?

Back

The area A of a circle is given by A(r) = πr², where r is the radius.

Front

If the area of a circle increases from 9π to 16π, what is the increase in radius?

Back

The radius increases from 3 to 4, which is an increase of 1.

Front

What set represents integers that are at least 7 and less than 13?

Back

The set is {7, 8, 9, 10, 11, 12}.

Front

How do you evaluate a function at a specific point?

Back

To evaluate f(x) at a point, substitute the value of x into the function. For example, f(-3) = 2(-3)² - 3 = 15.

Front

What is the distance function for a car moving with a quadratic equation?

Back

The distance d(t) = 60t - 2t² describes the car's distance from its starting point after t hours.

Front

How do you find when a car returns to its starting point using a distance function?

Back

Set the distance function equal to zero and solve for t. For d(t) = 60t - 2t², it returns to the starting point at t = 30.

Front

What does the inequality 2 ≤ 3y < 4 represent?

Back

It represents the range of values for y that satisfy both inequalities, which is [⅔, ⅓).

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function in the form f(x) = ax² + bx + c is the point (h, k) where h = -b/(2a) and k = f(h).

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.