Graphing Absolute Value Functions Warmup

Choose the correct equation for the graph.

Answer explanation

The correct equation is \(y=|x|+2\) because it represents a V-shaped graph that opens upwards and is shifted 2 units up on the y-axis, matching the characteristics of the graph in the question.

Choose the correct equation for the graph.

Answer explanation

The correct equation is \(y=|x|-2\) because it represents a V-shaped graph that opens upwards, shifted down by 2 units. The vertex is at (0, -2), matching the characteristics of the graph in the question.

Choose the correct equation for the graph.

Answer explanation

The correct equation is \(y=|x+2|\) because it represents a V-shaped graph that opens upwards with its vertex at (-2, 0), matching the characteristics of the graph in the question.

Choose the correct equation for the graph.

Answer explanation

The correct equation is \(y=|x-2|\) because it represents a V-shaped graph with a vertex at (2,0), matching the characteristics of the graph in the question.

What is the domain of the absolute value function?

• (4, 0)

• (0, 4)

• (-infinity, infinity)

• [4, infinity)

Answer explanation

The domain of the absolute value function is all real numbers, as it can take any input. Therefore, the correct choice is (-infinity, infinity), which includes all possible values.

If the "a" value is less than (<) 0, what kind of transformation will happen?

• vertical stretch by a factor of 1

• vertical compress by a factor of 1

• reflection across the x-axis

• horizontal shift to the right

Answer explanation

If the 'a' value is less than 0, it indicates a reflection across the x-axis. This means that the graph of the function will be flipped over the x-axis, changing the sign of the output values.