Suppose f(x)=3x+5. describe how the graph of each function compares to f. 1) g(x)=f(x)+12 2) h(x)=f(x)-7 3) g(x)=f(x=8) 4) h(x)=f(x-14) 5) g(x)=4f(x) 6) g(x)=f(5x)

Function transformation involves changing the form of a function

The function is given as:

1. g(x) = f(x) + 12

This gives

g(x) = f(x) + 12 relates to f(x) by shifting f(x) 12 units up

2. h(x) = f(x) - 7

This gives

h(x) = f(x) - 7 relates to f(x) by shifting f(x) 7 units down

3. g(x) = f(x + 8)

This gives

g(x) = f(x + 8) relates to f(x) by shifting f(x) 8 units left

4. h(x) = f(x - 14)

This gives

h(x) = f(x - 14) relates to f(x) by shifting f(x) 14 units right

5. g(x) = 4f(x)

This gives

g(x) = 4f(x) relates to f(x) by vertically stretching f(x) by a factor of 4

6. h(x) = f(5x)

This gives

h(x) = f(5x) relates to f(x) by horizontally stretching f(x) by a factor of 5

Read more about function transformations at:

link

1)

g(x) = f(x)+12 represents translating f(x) 12 units up to get g(x). This is because y = f(x), so we're effectively adding 12 to each y coordinate of the points on f(x) to have them move to the points on g(x).

note: the term "translating" is another way of saying "shifting" or "sliding".

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2)

h(x) = f(x)-7 means translating f(x) 7 units down to get h(x). We use the same reasoning as in problem 1. The general form is h(x) = f(x)+k, and in this case, k = -7. The negative k value tells us to shift down.

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3)

g(x) = f(x+8) means we translate 8 units to the left. The general template is g(x) = f(x-h). If h > 0, then we shift right. If h < 0, then we shift left. The amount that is shifted is equal to the absolute value of h.

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4)

h(x) = f(x-14) tells us to shift f(x) 14 units to the right. Same idea as problem 3, but now h = 14.

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5)

g(x) = 4*f(x) means we vertically stretch f(x) by a factor of 4. Since y = f(x), we are effectively doing g(x) = 4*f(x) = 4*y, which pulls the y coordinates upward by a factor of 4. A point like (1,2) will jump to (1,8) after multiplying the y coordinate by 4.

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6)

g(x) = f(5x) tells us to horizontally compress f(x) by a factor of 5. The general template is g(x) = f(a*x) where the 'a' determines horizontal stretching or compression. If , then we have horizontal stretching going on. If , then we'll have horizontal compression.

the answer should be 3.54 g/cm^3