Math

QuestionIdentify the equation of the vertically stretched and shifted absolute value function: 3 left, 8 down. Options: a. f(x)=2x+38f(x)=2|x+3|-8 b. f(x)=12x+38f(x)=\frac{1}{2}|x+3|-8 c. f(x)=2x=38f(x)=2|x=3|-8 d. f(x)=12x38f(x)=\frac{1}{2}|x-3|-8

Studdy Solution

STEP 1

Assumptions1. The absolute value parent function is f(x)=xf(x) = |x| . The function is vertically stretched, which implies a multiplication factor greater than13. The function is shifted3 units to the left, which implies a change in the x-value inside the absolute value function4. The function is shifted8 units down, which implies a subtraction from the overall function

STEP 2

The general form of a transformed absolute value function is f(x)=abx+c+df(x) = a|bx+c|+d, where- aa is the vertical stretch or compression factor. If a>1a>1, it is a stretch; if 0<a<10<a<1, it is a compression. - bb is the horizontal stretch or compression factor. If b>1|b|>1, it is a compression; if 0<b<10<|b|<1, it is a stretch. - cc is the horizontal shift. If c>0c>0, it is a shift to the left; if c<0c<0, it is a shift to the right. - dd is the vertical shift. If d>0d>0, it is a shift up; if d<0d<0, it is a shift down.

STEP 3

Given that the function is vertically stretched, the value of aa should be greater than1.

STEP 4

Given that the function is shifted3 units to the left, the value of cc should be3.

STEP 5

Given that the function is shifted8 units down, the value of dd should be -8.

STEP 6

Considering the above information, the equation of the function should be of the form f(x)=abx+38f(x) = a|bx+3|-8, where a>1a>1.

STEP 7

Comparing the above form with the given options, we can see that only option a. f(x)=2x+3f(x)=2|x+3|- fits the criteria.
So, the equation that could represent this function is f(x)=2x+3f(x)=2|x+3|-.

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