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Kipish [7]
3 years ago
12

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)
Mathematics
1 answer:
Lubov Fominskaja [6]3 years ago
6 0

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".

===================================================

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.

===================================================

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.

===================================================

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.

===================================================

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.

===================================================

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 0 \le a \le 1, then we have horizontal stretching going on. If a > 1, then we'll have horizontal compression.

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asambeis [7]

<u>Answer:</u>

The correct answer option is D. -5^x+3x-2

<u>Step-by-step-explanation:</u>

We are given the following two functions:

f(x)=-5^x-4

and

g(x)= -3x-2

We are to find (f-g)(x) so we will subtract the function g from function f, arrange the like terms together and combine them like shown below to get:

(f-g)(x) =(-5^x-4)-(-3x-2)

(f-g)(x)=-5^x-4+3x+2

(f-g)(x)=-5^x+3x-2

Therefore, (f-g)(x) is equal to -5^x+3x-2 so the correct answer option is D. -5^x+3x-2.

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Answer:

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Step-by-step explanation:

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The number of walls, w, that Joe can paint in t hours is given by the equation w=32t−1. Answer the questions below.
klio [65]

We have been given an equation w=\frac{3}{2}t-1 that represents umber of walls, w, that Joe can paint in t hours. We are asked to find the number of hours it will take Joe yo paint 7 walls.

To solve our given problem, we will substitute w=7 in our given equation as:

7=\frac{3}{2}t-1

Let us solve for t.

7+1=\frac{3}{2}t-1+1

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8\cdot\frac{2}{3}=\frac{2}{3}\cdot\frac{3}{2}t

\frac{8\cdot2}{3}=t

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3 years ago
Write a linear equation that is parallel to
san4es73 [151]

Answer:

2y=11 - 5x

Step-by-step explanation:

An equation that is parallel shares the same gradient thus

2y= -5x - 8

y = -5/2x- 4

gradient m = -5/2

substitute value of m and the co-ordinates into a new linear equation

y = mx + c

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c = 20-9 = 11

thus y = -5/2x + 11

2y=11 - 5x

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