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.
