Question

Which of the following transforms the graph of y=x^2 to the graph of y=x^2-7?
A.a translation 7 units to the right
B. a translation 7 units to the left
C. translation 7 units down
D.a translation 7 units up

Answer 1

You're performing this kind of transformation:

$f(x)\mapsto f(x)+k$

This kind of transformations translate the functions vertically k units up if k is positive, k units down if k is negative.

So, in your case, you translate the function 7 units down.

Answer 2

The correct option for the question "Which of the following transforms the graph of y=x^2 to the graph of y=x^2-7?" is C: translation 7 units down

The given equation representing the graph is:

$y = x^2$

The equation $y = x^2$ becomes $y = x^2 - 7$ after transformation

Note that:

When a function representing the graph y = f(x) becomes y = f(x) - a after translation, it means the graph f(x) has been translated "a" units down

Therefore since the function $y = x^2$ becomes $y = x^2 - 7$ after translation, it means that the graph $y = x^2$ undergoes a translation of 7 units down

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