Write a function g whose graph represents the indicated transformation of the graph of f. (5 Questions)

Question

1. f(x) = 4x + 1; translation 2 units left

2. f(x) = -4|x - 2|; vertical shrink by a factor of 1/2

3. Let g be a translation 4 units down and a horizontal shrink by a factor of 1/4 of the graph of f(x) = x

4. Let g be a reflection in the x-axis and a vertical stretch by a factor of 3, followed by a translation 4 units down and 1 unit right of the graph of f(x) = |x|

5. The total reimbursement (in dollars) for driving a company car m miles can be modeled by the function f(x) = 0.45m + 5. After a policy change, five more dollars are added on and then the total reimbursement amount is multiplied by 1.25. Describe how to transform the graph of f. What is the total reimbursement for a trip of 95 miles?

Answer 1

The general rules of transformations are a f(b(x+h)) + k

k - vertical shift up/down

h - horizontal shift down/up (the opposite) - So a positive h=3 means a horizontal shift left (negative) 3 spaces.

a - vertical stretch/shrink. Negative a is reflection over x-axis.

b - horizontal shrink/stretch (the opposite) - So b=3 is a horizontal shrink of 1/3. Negative b is reflection over y-axis. (Your problems aren't using this one.)

1. g(x) = f(x-2) = 4(x-2) + 1

2. g(x) = 1/2f(x) = -2|x - 2|

3. g(x) = 1/4f(x) - 4 = x/4 - 4

4. g(x) = -3f(x-1) - 4 = -3|x-1| - 4 This phrase "followed by" can be confusing. In this case, it doesn't make any difference, you need to put the x-1 inside the function to make it shift right.

5. g(m) = 1.25 (f(m) + 5) = 1.25 (0.45m + 5 + 5) Here the phrase "then" does make a difference. You are adding the 5 dollars then multiplying by 1.25, so I had add to those extra parentheses. For 95 miles, I get $65.94 rounded to nearest cent.