Question

current learning objective: graphing transformations of exponential functions
question 12 practice similar questions
score: 0 of 1 point
the graph of the function ( f(x)=5^{x}-4 ) can be obtained from the graph of ( g(x)=5^{x} ) by which one of the following actions:
a shifting the graph of ( g(x) ) upward 4 units
b shifting the graph of ( g(x) ) to the right 4 units
c shifting the graph of ( g(x) ) downward 4 units
d shifting the graph of ( g(x) ) to the left 4 units
is the domain of the function ( f(x) ) still ( (-infty, infty) )?
a yes
b no
the range of the function ( f(x) ) is ( (a, infty) ).
the value of ( a ) is enter your answer
submit answer attempts: 0/3
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Explanation:

Step1: Recall vertical shift rule

For a function \(y = g(x)+k\), if \(k>0\) it shifts up \(k\) units, if \(k < 0\) it shifts down \(|k|\) units. Here \(f(x)=g(x)-4\), so it shifts down 4 units.

Step2: Check domain

The domain of an exponential function \(y = a^{x}+b\) (\(a>0,a
eq1\)) is still \((-\infty,\infty)\) because we can substitute any real - number \(x\) into \(a^{x}\).

Step3: Find range

The range of \(y = 5^{x}\) is \((0,\infty)\). For \(y=5^{x}-4\), we subtract 4 from each value in the range of \(y = 5^{x}\). So the range is \((- 4,\infty)\)

Answer:

C. shifting the graph of \(g(x)\) downward 4 units
A. Yes
\(-4\)