Which is the graph of parent function f(x)=2^x

Mathematics

2 answers:

olga nikolaevna [1]3 years ago

8 0

Option D is the correct answer

navik [9.2K]3 years ago

3 0

Answer:

Graph D

Step-by-step explanation:

$f(x)= 2^x$

Given f(x) is a exponential function

The graph (a) is a graph of an absolute function because we have V shaped graph

The graph (b) is the graph of a line so it is a graph of a linear function

The graph (c) is a U shaped graph. U shaped graph is a graph of a quadratic function.

The graph (d) is a curve shaped graph. It is a graph of an exponential function.

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Vikki [24]

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2 years ago

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notka56 [123]

$\dfrac{2}{\sqrt3\cos x+\sin x}=\sec\left(\dfrac{\pi}{6}-x\right)\\\\\dfrac{2}{\sqrt3\cos x+\sin x}=\dfrac{1}{\cos\left(\dfrac{\pi}{6}-x\right)}\ \ \ \ \ (*)\\----------------\\\\\cos\left(\dfrac{\pi}{6}-x\right)\ \ \ \ |\text{use}\ \cos(x-y)=\cos x\cos y+\sin x\sin y\\\\=\cos\dfrac{\pi}{6}\cos x+\sin\dfrac{\pi}{6}\sin x=\dfrac{\sqrt3}{2}\cos x+\dfrac{1}{2}\sin x=\dfrac{\sqrt3\cos x+\sin x}{2}\\------------------------------$

$(*)\\R_s=\sec\left(\dfrac{\pi}{6}-x\right)=\dfrac{1}{\cos\left(\dfrac{\pi}{6}-x\right)}=\dfrac{1}{\dfrac{\sqrt3\cos x+\sin x}{2}}\\\\=\dfrac{2}{\sqrt3\cos x+\sin x}=L_s$