Question

On a separate piece of graph paper, graph y = -|x| + 1; then click on the graph until the correct one appears.

Answer 1

Answer: The correct option is 4.

Explanation:

The given equation is,

$y=-|x|+1$

This is a form of a modulus function, therefore shape of graph is V.

The graph of |x| is a upward v-shaped graph lies on origin.

$f(x)=|x+a|+b$

Where a represents horizontal shift and b represents vertical shift.

If a>0, then graph of |x| shifts left side. If a<0, then graph of |x| shifts right side.

If b>0, then graph of |x| shifts upward. If b<0, then graph of |x| shifts right downward.

In the given function -|x| means reflection along the x-axis and addition of 1 means the graph will shift in upward direction as shown in below figure.

The other way to choose the correct option is, find the y-intercept.

Putting  x=0 in given equation we get y=1. So, the y intercepts is (0,1) which is sown in last figure only.

Therefore, the option 4 is correct.

Answer 2

(see attachment)

The third graph $y=-|x|+1$ is the correct one, since the peak of the line is over the x-axis.