Question

PLEASE HELP ASAP MATH!!! :(

1) What transformation takes the graph of f(x)=4x+9 to the graph of g(x)=4x+7 ?
translation 2 units up
translation 2 units right
translation 2 units down
translation 2 units left
(first picture)

2) The graph of function g is a vertical stretch of the graph of function f ​​by a factor of 3.
Which equation describes function g?
​​ g(x)=1/3f(x)
​​ g(x)=f(x/3)
g(x)=3f(x)
​​ g(x)=f(3x)
(second picture)

Answer 1

1) What transformation takes the graph of f(x)=4x+9 to the graph of g(x)=4x+7 ?

Both have same slope = 4

f(x)=4x+9 , y - intercept b = 9

g(x)=4x+7, y - intercept b = 7; 2 units down from f(x)

Answer

translation 2 units down

2) The graph of function g is a vertical stretch of the graph of function f ​​by a factor of 3.

Which equation describes function g?

Vertically stretch | a |  > 1

Stretch by factor of 3 so f(x) = 3f(x)

Answer

g(x) = 3f(x)

Answer 2

1. Translation 2 units down
2. g(x) = 3f(x)

Further explanation

Translation and stretching are forms of geometrical transformation.

Given c ∈ R, after the transformation coordinates of each point, (x, y) on the graph of y = f(x) change as follows:

Horizontal shift  

• function: $\boxed{ \ y = f(x + c) \ }$ translation c units left
• coordinates: $\boxed{ \ (x - c, y) \ }$ translation c units left

Vertical shift

• function: $\boxed{ \ y = f(x) + c \ }$ translation c units up
• coordinates: $\boxed{ \ (x, y + c) \ }$ translation c units up

Horizontal stretch

• function: $\boxed{ \ y = f(cx) \ }$ horizontal stretch by a factor of c
• coordinates: $\boxed{ \ (\frac{x}{c}, y) \ }$ horizontal stretch by a factor of c

Vertical stretch

• function: $\boxed{ \ y = cf(x) \ }$ vertical stretch by a factor of c
• coordinates: $\boxed{ \ (x, cy) \ }$ vertical stretch by a factor of c

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Problem No.1

$\boxed{ \ f(x) = 4x + 9 \ } \rightarrow \ ? \rightarrow \boxed{ \ g(x) = 4x + 7 \ }$

Clearly, to obtain the graph of $\boxed{ \ g(x) = 4x + 7 \ }$ we shift the graph of $\boxed{ \ f(x) = 4x + 9 \ }$ downward 2 units.

• $\boxed{ \ f(x) = 4x + 9 \ }$ translation 2 units down.
• $\boxed{ \ f(x) = (4x + 9) - 2 \ }$
• $\boxed{ \ g(x) = 4x + 7 \ }$

Thus. the transformation that takes the graph $\boxed{f(x) = 4x + 9}$ to the graph $\boxed{g(x) = 4x + 7}$ is the translation 2 units down.

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Problem No.2

$\boxed{ \ f(x) \ } \rightarrow \ ? \rightarrow \boxed{ \ g(x) = 3f(x) \ }$

Clearly, to obtain the graph of $\boxed{ \ g(x) = 3f(x) \ }$ we stretch vertically the graph of $\boxed{ \ f(x) \ }$ by a factor of 3 (multiply each y-coordinate by 3).

Thus. the equation describes function g is $\boxed{ \ g(x) = 3f(x) \ }$, that is, a vertical stretch of the graph of function f ​​by a factor of 3.

Learn more

1. Which phrase best describes the translation from the graph y = 2(x – 15)² + 3 to the graph of y = 2(x – 11)² + 3? https://brainly.com/question/1369568  
2. Which equation represents the new graph? https://brainly.com/question/2527724  
3. What transformations change the graph of (f)x to the graph of g(x)? https://brainly.com/question/2415963

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