Question

8. Which of the following statements are true for the absolute value function f(x) = - 1/5x-1|-7I.The graph has a horizontal shift left 1 units.II. The graph has a vertical shift down 7 units.III. The graph shrinks because 1/5 is less than 1.

Answer 1

II, III and IV

Explanation:

We have a function in the following format:

f(x) = a*|x + b| + c

If |a| > 1, the function is extended. If |a| < 1, it shrinks. If a is negative, the function flips.

b is related to the horizontal shifts. If b > 0, the function shifts to the left b units. If b < 0, the function shifts to the right b units.

c is related to the vertical shifts. If c > 0, the function has a vertical shift up c units. If c < 0, the function has a vertical shift down c units.

In our question:

f(x) = (-1/5)*|x - 1| - 7

So

a = 1/5

b = -1

c = -7

|a| = 1/5, which means that the function shrinks, so the third option is correct. a is negative, which means that the function flips. So option IV is correct

b = -1 means that the horizontal shift is of 1 unit to the right. So the option I is wrong.

c = -7 means that the graph has a vertical shift down 7 units. So option II is correct.

The correct answer is:

II, III and IV