Question

f(x) = 2|x+3| – 5, name the type of function and describe each of the three transformations from the parent functionf(x) = |x|

Answer 1

1. absolute value function
2. expanded vertically by a factor of 2
3. shifted horizontally by 3 units to the left
4. shifted down by 5 units

Explanation:

The transformations generally applied to a function f(x) can be generically written as ...

g(x) = a·f(b·x -c) +d

where ...

• a = vertical expansion factor
• b = horizontal compression factor
• c = horizontal shift (translation) right
• d = vertical shift (translation) up

Your f(x) is |x|, the absolute value of x. The various transformation factors applied to it are ...

• a = 2; vertical expansion by a factor of 2
• b = 1; no horizontal compression
• c = -3; horizontal shift left by 3 units
• d = -5; vertical shift down by 5 units

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Comment on the above generic form

In the form shown, the expansion and compression factors are applied before the translations horizontally and vertically. When the expansion/compression factors are negative, the function is reflected across the x- and/or y-axis, respectively.