Question

Fill in the informationFor each function, choose whether it’s graph opens upward or downward. Choose the equation with the widest graph.Choose the equation with the narrowest graph.

Answer 1

We have the function:

y = |x|

And its graph (in blue):

From this graph, we see that:

y = 1 |x| opens upwards

We know that if we multiply a function by a constant non-zero (and positive) factor, it shrinks or expands horizontally. If this factor is less than 1, then it expands; otherwise, it shrinks. For the function:

y = |x|/3

We see that 1/3 < 1, so its graph is wider than the |x| function.

Now, for y = 3|x|, we see that 3 > 1, so its graph is narrower than |x|.

But if we multiply by a negative number, the function expands or shrinks and, additionally, it is reflected with respect to the x-axis. For the function y = -|x|/2, we see that it expands and gets reflected.

Summarizing:

y = |x| opens upwards

y = |x|/3 opens upwards and is the widest

y = 3|x| opens upwards and is the narrowest

y = -|x|/2 opens downwards