Absolute value graphs

Front

What is the parent function of absolute value graphs?

Back

The parent function of absolute value graphs is y = |x|.

Front

How does the graph of y = |x| + k transform the parent function?

Back

The graph shifts vertically by k units. If k is positive, it shifts up; if k is negative, it shifts down.

Front

What effect does a negative sign in front of the absolute value have on the graph?

Back

It reflects the graph across the x-axis.

Front

What does the coefficient in front of the absolute value function (e.g., y = a|x|) affect?

Back

It affects the width of the graph. If |a| > 1, the graph is narrow; if |a| < 1, the graph is wide.

Front

How does the graph of y = |x - h| transform the parent function?

Back

The graph shifts horizontally by h units. If h is positive, it shifts right; if h is negative, it shifts left.

Front

What is the effect of the transformation y = |x| - k?

Back

The graph shifts down by k units.

Front

If the graph of y = |x| is transformed to y = -|x|, what is the result?

Back

The graph is reflected over the x-axis.

Front

What does the term 'narrow' mean in relation to absolute value graphs?

Back

A 'narrow' graph has a steeper slope compared to the parent function, indicating a larger coefficient in front of the absolute value.

Front

What does the term 'wide' mean in relation to absolute value graphs?

Back

A 'wide' graph has a less steep slope compared to the parent function, indicating a smaller coefficient in front of the absolute value.

Front

How do you determine if a graph is 'narrow' or 'wide'?

Back

Compare the coefficient of the absolute value function to 1. If it's greater than 1, it's narrow; if less than 1, it's wide.