@) brainliest for whoever can me faster which statement correctly describes the relationship between the graph of f(x) and the graph of g(x)=f(x)+3 ? the graph of g(x) is the graph of f(x) translated 3 units right. the graph of g(x) is the graph of f(x) translated 3 units left. the graph of g(x) is the graph of f(x) translated 3 units up. the graph of g(x) is the graph of f(x) translated 3 units down . which statement correctly describes the relationship between the graph of f(x) and g(x)=f(x−7) ? the graph of g(x) is the graph of f(x) translated 7 units left. the graph of g(x) is the graph of f(x) translated 7 units right. the graph of g(x) is the graph of f(x) translated 7 units down. the graph of g(x) is the graph of f(x) translated 7 units up. the graph of g(x) is the graph of f(x)=x+9 reflected across the y-axis. which equation describes function g? g(x)=x−9 g(x)=−x+9 g(x)=−9x+9 g(x)=−x−9 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)=3f(x) g(x)=f(3x) g(x)=13f(x) g(x)=f(x3) what transformation takes the graph of f(x)=2x+3 to the graph of g(x)=2x+4 ? translation 1 unit left translation 1 unit up translation 1 unit down translation 1 unit right

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.

how is that middle school

step-by-step explanation: