Question

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Answer 1

Answer:

1) f(x) = 4x and g(x) = f(x) + 3

Answer: the graph of g(x) is the graph of f(x) translated 3 units up.

2) g(x) = f(x+2)

Answer: the graph of g(x) is the graph of f(x) translated two units left.

Step-by-step explanation:

Answer 2

Answers:

1) Third option: The graph of g(x) is the graph of f(x) translated 3 units up.

2) Second option: The graph of g(x) is the graph of f(x) translated 7 units right.

3) Second option: g(x)=-x+9

4) First option: g(x)=3f(x)

5) Second option: translation 1 unit up

Solution:

1) f(x); g(x)=f(x)+3

When we add to a function a value, the graph of the new function is the graph of the original function translated the value in units upward. In this case g(x)=f(x)+3, we are adding 3 units to f(x), then the graph of g(x) is the graph of  f(x) translated 3 units up.

2) f(x); g(x)=f(x-7)

When we subtract a value to x, the graph of the new function is the graph of the original function translated the value in units to the right. In this case g(x)=f(x-7), we are subtracting 7 units to x, then the graph of g(x) is the graph of f(x) translated 7 units to the right.

3) The graph of g(x) is the graph of f(x)=x+9 reflected across the y-axis.

To reflex a graph across the y-axis we must change x by -x in the original function, then:

g(x)=f(-x)

g(x)=(-x)+9

g(x)=-x+9

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

To do a vertical strecth the graph of a function by a factor, we must multiply the original function by the factor. In this case the factor is 3, then:

g(x)=3f(x)

5) What transformation takes the graph of f(x)=2x+3 to te graph of g(x)=2x+4

We can write g(x) as (4=3+1):

g(x)=2x+3+1

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

and 2x+3=f(x)

g(x)=f(x)+1

Then we are adding 1 unit to f(x), then the graph of g(x) is the graph of  f(x) translated 1 unit up.