Module 5 Test Form A2: Nonlinear Functions

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different intervals of the input variable.

Front

How do you evaluate a piecewise function?

Back

To evaluate a piecewise function, determine which interval the input value falls into and use the corresponding expression to find the output.

Front

What is the formula for the function f(x) = {-x + 3; x < 0, 2x + 3; x > 0}?

Back

This is a piecewise function where f(x) = -x + 3 for x < 0 and f(x) = 2x + 3 for x > 0.

Front

Evaluate f(-1) for the function f(x) = {-x + 3; x < 0, 2x + 3; x > 0}.

Back

f(-1) = -(-1) + 3 = 4.

Front

What is the graph of a piecewise function?

Back

The graph of a piecewise function consists of different segments, each corresponding to a different piece of the function.

Front

What does the notation f(x) = -2 if x ≤ 0 mean?

Back

It means that for any value of x that is less than or equal to 0, the output of the function f(x) is -2.

Front

What is the significance of the axis of symmetry in a graph?

Back

The axis of symmetry is a vertical line that divides the graph into two mirror-image halves.

Front

For the function g(x) = -3|x - 2| + 4, what is the vertex?

Back

The vertex is the point (2, 4), which is the highest point of the graph since it opens downwards.

Front

What is the range of the function g(x) = -3|x - 2| + 4?

Back

The range is y < 4, meaning the output values can be any number less than 4.

Front

How do you identify key features of a graph?

Back

Key features include the vertex, axis of symmetry, intercepts, and the overall shape of the graph.