Beth says that the graph of g(x) = + 1 is a translation of 5 units to the left and 1 unit up of f(x) = . She continues to explai

Question

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Beth says that the graph of g(x) = + 1 is a translation of 5 units to the left and 1 unit up of f(x) = . She continues to explai

n that the point (0, 0) on the square root function would be translated to the point (–5, 1) on the graph of g(x). Is Beth’s description of the transformation correct? Explain.

Mathematics

1 answer:

Nata [24] · Answer 1 · 2023-09-04T20:28:24+03:00

Beth's description of the transformation is incorrect

<h3>Complete question</h3>

Beth says that the graph of g(x)=x-5+1 is a translation of 5 units to the left and 1 unit up of f(x) = x. She continues to explain that the point (0,0) on the square root function would be translated to the point (-5,1) on the graph of g(x). Is Beth's description of the transformation correct? Explain

<h3>How to determine the true statement?</h3>

The functions are given as:

g(x) = x - 5 + 1

f(x) = x

When the function f(x) is translated 5 units left, we have:

f(x + 5) = x + 5

When the above function is translated 1 unit up, we have:

f(x + 5) + 1 = x + 5 + 1

This means that the actual equation of g(x) should be

g(x) = x + 5 + 1

And not g(x) = x - 5 + 1

By comparison;

g(x) = x - 5 + 1 and g(x) = x + 5 + 1 are not the same

Hence, Beth's description of the transformation is incorrect