Question

current learning objective: graphing transformations of exponential functions
question 11 practice similar questions
score: 0 of 1 point
which sequence of transformations will yield the graph of ( g(x)=7^{x - 3}+9 )
a horizontal shift 3 units to the right; vertical shift 9 units down
b horizontal shift 9 units to the right; vertical shift 3 units upwards
c horizontal shift 3 units to the left; vertical shift 9 units upwards
d horizontal shift 9 units to the left; vertical shift 3 units down
e horizontal shift 3 units to the right; vertical shift 9 units upwards
f horizontal shift 3 units to the left; vertical shift 9 units down
submit answer attempts: 0/4
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Explanation:

Step1: Recall transformation rules

For an exponential function \(y = a^{x - h}+k\), a horizontal shift of \(h\) units (right if \(h>0\), left if \(h < 0\)) and a vertical shift of \(k\) units (up if \(k>0\), down if \(k < 0\)).
For the function \(g(x)=7^{x - 3}+9\), here \(h = 3\) and \(k=9\).

Step2: Determine the shifts

Since \(h = 3>0\), there is a horizontal shift of \(3\) units to the right. Since \(k = 9>0\), there is a vertical shift of \(9\) units upwards.

Answer:

E. Horizontal shift 3 units to the right; Vertical shift 9 units upwards