Hey can someone help pls

Question

A. The graph of f is shifted 3 units up to create the graph of g.

B. The graph of f is steeper than the graph of g.

C. The graph of f is shifted 3 units down to create the graph of g.

D. The graph of f is less steep than the graph of g.

For choice A this transformation would be written as g(x)=__

For choice B this transformation would be written as g(x)=__

For choice C this transformation would be written as g(x)=__

For choice D this transformation would be written as g(x)=__

Answer 1

A. f+3 = g, f(x)+3 = g(x)

B. f(x) = mx, g(x)=nx, where n<m or f(x)>g(x) if x>0, but f(x)<g(x) if x<0

C. f-3=g f(x)-3 = g(x)

D. f(x)=mx, g(x)=nx where m<n or f(x)<g(x) if x>0 but f(x)>g(x) if x<0

Answer 2

When f is shifted 3 units up to create the graph of g, each output value of f increases by 3 units to form the corresponding output in g. For the function f, if x is the input , then f(x) the output.

Therefore,

(A) g(x) = f(x) + 3

When the graph of f is steeper than the graph of g - this means that the graph of g is less steeper as compared to the graph of f . For example, if f(x) is a linear function with slope m, then g(x) is a linear function with slope n < m.

If f(x) is a quadratic function with a co-efficient M, then g(x) will be the quadratic function with the co-efficient M /N where N ≠ 0 and N > M and the graph of g(x) is not as sharp a U shape as compared to f(x)

Yeah, to keep it simple, in general, we can say that g is compressed by a factor a = M/ N, and of course a<1.

Therefore,

(B) g(x) = a f(x)

For example if f(x) = x, then g(x)=(1/2) f(x) ; if f(x)= 2x², then g(x) = (2/4) x²

which is equivalent to g(x)=(1/2)x².

When the graph of f is shifted 3 units down to create g- This is pretty straight forward and opposite situation to (A)

Therefore

(C) g(x) = f(x) -3

When the graph of f is less steep, than the graph of g - This is a situation opposite to that in (B) :- this means that the graph of g is steeper than the graph of f which means the same as saying g is vertically stretched .

Therefore,

(D) g(x) = b f(x) , where b = M•N ( M, N as in case B)

For example, if f(x) = x, then g(x) = 2x ; if f(x) = 2x², then g(x) = 6x².