Graphing Logarithmic Functions — Quiz

Question 9 • Algebraic Reasoning

Which statement is true?

Answer

The graph of y is equal to log sub b of x plus 4 is the graph of y is equal to log sub b of x translated 4 units up.

The graph of y is equal to log sub b of x minus 4 is the graph of y is equal to log sub b of x translated 4 units left.

The graph of y is equal to log sub b of open paren x minus 4 close paren is the graph of y is equal to log sub b of x translated 4 units down.

The graph of y is equal to log sub b of open paren x plus 4 close paren is the graph of y is equal to log sub b of x translated 4 units right.

Explanation

Adding 4 outside the logarithm changes every output value by 4: y = log_b(x) + 4 shifts the graph of y = log_b(x) up 4 units. Changes inside the logarithm shift the graph horizontally instead, so the other statements describe the wrong direction or type of shift.

AI-written and checked against the verified answer.

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