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Setler79 [48]
3 years ago
13

What are the domain and range of the exponential function below?

Ex%2B6" id="TexFormula1" title="F(x) = 5^x+6" alt="F(x) = 5^x+6" align="absmiddle" class="latex-formula">

Mathematics
1 answer:
faust18 [17]3 years ago
3 0

Answer:

B

Step-by-step explanation:

The domain is the set of x values for which the function is defined.

The range is the set of y values for which the function is defined.

Attached is the graph of the exponential function.

It is the basic graph of exponential function of y = 5^x which is shifted 6 units above (because of +6 at the end).

<em><u>Looking at the graph, the domain is the set of all x values.</u></em>

<em><u>The range is anything above 6.</u></em>

Correct answer is B.

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Step-by-step explanation:

Given:

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1. Consider triangle NLM. This is a right triangle, because NL ⊥ LM. In this triangle,

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So,

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Also

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So,

\sin \angle KNL=\dfrac{\text{opposite leg}}{\text{hypotenuse}}=\dfrac{KL}{LN}=\dfrac{KL}{45\tan 50^{\circ}}\\ \\KL=45\tan 50^{\circ}\sin 50^{\circ}\approx 41.08

and

\cos \angle KNL=\dfrac{\text{adjacent leg}}{\text{hypotenuse}}=\dfrac{KN}{LN}=\dfrac{KN}{45\tan 50^{\circ}}\\ \\KN=45\tan 50^{\circ}\cos 50^{\circ}=45\sin 50^{\circ}\approx 34.47

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