Need help ASAP! Thank you

Question

1. Transformations

1a. Explain the different transformations for f(x + 2) and f(x) + 2.

1b. Use the f(x) give n below to determine the transformed functions

f(x) = 3x + 1

f(x + 2) =

f(x) + 2 =

1c. Include a graph for each function on the same graph.

1d. Find -f(x) for f(x) = 2x - 5

2(1). A swimming pool is being drained at a constant rate of 3 inches (depth of the

water) per hour. The depth of the water after 5 hours is 32 inches. Write the equation

for this function in point slope form.

2(1)b. Graph your function to find out how long it will take to empty the pool completely.

3(1). What is the new function resulting from applying a horizontal shrink by 1/3 to f(x)= |x - 1| + 3.

Answer 1

Hi,

1a. Explain the different transformations for and f(x) + 2.

f(x) + 2 it means the graph shift to the up as 2 an units

f(x + 2) it means the graph will shift to the left as 2 an units

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1b. Use the f(x) give n below to determine the transformed functions

f(x) = 3x + 1

f(x + 2) = 3(x+2) +1 = 3x + 7

f(x) + 2 = 3x+1 +2 = 3x + 3

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. Find -f(x) for f(x) = 2x - 5

-f(x) = -( 2x-5) = -2x + 5 it means new function is reflect of given function respect to the x-ax

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2(1). A swimming pool is being drained at a constant rate of 3 inches (depth of the

water) per hour. The depth of the water after 5 hours is 32 inches. Write the equation

for this function in point slope form.

in fact slope is -3 because drain ------> f(h) = -3h + b given information is h=5 and f(h) = 32 so replace this information to the function for finding b

32= -3*5 + b ------> b = 47 as a result f(h) = -3h + 47

2(1)b. Graph your function to find out how long it will take to empty the pool completely.

it means f(h) = 0 ------ - 3h + 47 = 0 ----> h = 47/3 it means after 47/3 hours it will be empty.

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3(1). What is the new function resulting from applying a horizontal shrink by 1/3 to f(x)= |x - 1| + 3

it means : new function is g(x) = 3| x - 1/3| + 3 or g(x) = | 3x-1| + 3

BECAUSE

f(1) = 3 g(1/3) = 3

f(3) = 5 g(1) = 3|1-1/3| +3 = 5 or |3*1 -1 | + 3 = 5

f(6) = 8 g(2) = 3|2-1/3| + 3 = 8 or |3*2 -1| +3 = 8

I hope it is useful,

Minoo