Looking at all the given transformations, the only one that does not belong with the other 3 is; C: stretch f(x) = x + 3 vertically by a factor of 2.
How to carry out Transformations?
1) We want to translate f(x) = 2x + 3 by 2 units upwards.
Now, when translating upwards it means that the y value increases by the number of units it is being translated upwards. Thus, our function after translation will now be;
f'(x) = 2x + 3 + 2
f'(x) = 2x + 5
2) We want to stretch f(x) = x + 3 vertically by a factor of 2.
Now, when stretching vertically by a factor, we simply multiply the function by that factor. Thus, our transformed graph should be;
f'(x) = 2(x + 3)
f'(x) = 2x + 6
3) We want to shrink f(x) = x + 5 horizontally by a factor of 1/2.
Now, when shrinking horizontally by a factor, we simply multiply the variable x by the inverse of that factor. Thus, our transformed graph should be;
f'(x) = (1/¹/₂)x + 5
f'(x) = 2x + 5
4) We want to translate f(x) = 2x + 3 by 1 unit to the left.
Now, when translating leftwards it means that the x value increases by the number of units it is being translated leftwards. Thus, our function after translation will now be;
f'(x) = 2(x + 1) + 3
f'(x) = 2x + 5
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