How do you shift exponential functions?

Shift the graph of f(x)=bx f ( x ) = b x left c units if c is positive and right c units if c is negative. Shift the graph of f(x)=bx f ( x ) = b x up d units if d is positive and down d units if d is negative.

Shift the graph of f(x)=bx f ( x ) = b x left c units if c is positive and right c units if c is negative. Shift the graph of f(x)=bx f ( x ) = b x up d units if d is positive and down d units if d is negative.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

a

step-by-step explanation: