Question

The graph of y = StartAbsoluteValue x EndAbsoluteValue is transformed as shown in the graph below. Which equation represents the transformed function?
On a coordinate plane, an absolute value function is shown. The vertex of the function is at (negative 3, negative 2). It crosses the x-axis at (negative 5, 0) and (negative 1, 0) and it crosses the y-axis at (0, 1).
y = StartAbsoluteValue x minus 3 EndAbsoluteValue + 2
y = StartAbsoluteValue x + 3 EndAbsoluteValue minus 2
y = StartAbsoluteValue x minus 2 EndAbsoluteValue + 3
y = StartAbsoluteValue x + 2 EndAbsoluteValue minus 3

Answer 1

Answer:

The equation is:

• $y=|x+3|-2$

Explanation:

The absolute value function is f(x) = |x|.

The vertex of the absolute value function is (0,0). That is its minimum point.

The vertex of the given function is (-3, -2).

That means that the graph of f(x) = |x| was translated 3 units to the left and 2 units downward.

A translation of 3 units to the left and 2 units downward tranforms f(x) into g(x) =  f(x + 3) - 2

Then, the new function will be: g(x) = |x + 3| - 2.

You can prove that that equation represents the three given points:

• g(-3) = |-3 + 3| -  2 = 0 - 2 = - 2 ⇒ (-3, - 2) $\checkmark$

• g(-5) = |-5 + 3} - 2 = 2 - 2 = 0 ⇒ (-5,0)  $\checkmark$

• g(-1) = |-1 + 3| - 2 = 2 - 2 = 0 ⇒(-1, 0) $\checkmark$

• g(0) = |0 + 3| - 2 = 3 - 2 = 1 ⇒ (0, 1) $\checkmark$

Conclusion

• The equation is    $y=|x+3|-2$

Answer 2

Answer:

B. on E2020

Step-by-step explanation: