Question

The graph of f(x) = |x| is transformed to g(x) = |x + 1| – 7. On which interval is the function decreasing?

(–∞, –7)
(–∞, –1)
(–∞, 1)
(–∞, 7)

Answer 1

Answer:

(−∞,−1) interval is is the function decreasing..

Step-by-step explanation:

Given : The graph of f(x) = |x|f(x)=∣x∣ is transformed to g(x) = |x+1|-7g(x)=∣x+1∣−7

To find : On which interval is the function decreasing?

Solution :

First we plot the graph of both the functions,

The graph of f(x) = |x|f(x)=∣x∣ is shown with black line.

The graph of g(x) = |x+1|-7g(x)=∣x+1∣−7 is shown with violet line.

The graph shows the interval over which it is increasing or decreasing.

As we notice it is increasing on the interval (-1,\infty)(−1,∞)

Decreasing on (-\infty,-1)(−∞,−1)

Therefore, (-\infty,-1)(−∞,−1) interval is the function decreasing.

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Answer 2

The function $g(x) =|x + 1| - 7$ decreases at interval $(-\infty, -1)$

The parent function is given as:

$f(x) =|x|$

The transformed function is given as:

$g(x) =|x + 1| - 7$

Both functions are absolute value functions, and an absolute value function is represented as:

$y=a| x-h |+k$

Where, the vertex of the function is:

$Vertex = (h,k)$

By comparing $y=a| x-h |+k$ and $g(x) =|x + 1| - 7$, we have:

$(h,k) = (-1,-7)$

$a= 1$

Because (a) has a positive value (i.e. 1) and (h) is negative, then the vertex represents a minimum.

This also means that, the function will decrease from infinity, till it gets to the x-coordinate of the vertex.

Hence, the function $g(x) =|x + 1| - 7$ decreases at interval $(-\infty, -1)$

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