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Graphs of Exponentials - Questions

Question 1
44098

Sketch the function \(y=2^x\) in the domain \(-2 \le x \le 2\)

Refer to worked solution

Question 2
44099

Sketch the function \(y=3^{-x}\) in the domain \(-2 \le x \le 2\)

Refer to worked solution

Question 3
44100

Sketch the function \(y=-4^{-x}\) in the domain \(-2 \le x \le 2\)

Refer to worked solution

Question 4
44101

Find the coordinates on the graph \(y=5^x\), where

i) \(x=-1\)
ii) \(y=25\)

i) \((-1,\dfrac{1}{5})\)  ii) \((2,25)\)

Question 5
44102

Find the intersections of the graphs of 

i) \(y=-4^x\) and \(y=-4\)
ii) \(y=3^{-x}\) and \(y=\dfrac{1}{9}\)

i) \((1,-4)\)   ii) \((2,\dfrac{1}{9})\)

Question 6
114254

Given that the points \((1,7)\) and \((0,1)\) lie on the exponential curve, find the equation of the curve. 

\(y=7^x\)

Question 7
114255

Given that the points \((2,9)\) and \((0,1)\) lie on the exponential curve, find the equation of the curve. 

\(y=3^x\)

Question 8
114256

Given that the points \((-2,16)\) and \((0,1)\) lie on the exponential curve, find the equation of the curve. 

\(y=4^{-x}\)

Question 9
13301

The exponential function in the adjacent graph has the equation:

A.

\(y = {2^x}\)

B.

\(y = - {\left( {\dfrac{1}{2}} \right)^x}\)

C.

\(y = - {2^x}\)

D.

\(y = {\left( {\dfrac{1}{2}} \right)^x}\)

\(y = {\left( {\dfrac{1}{2}} \right)^x}\)

The point \((-2,4)\) lies on the curve

In D, \( \quad y=\left(\dfrac{1}{2}\right)^x\)

\(\begin{aligned}
& \text { LHS }=4 \\
& \text { RHS }=\left(\frac{1}{2}\right)^{-2} \\
&=4 \\
&=\text { LHS } \\
& \therefore D
\end{aligned}\)

Question 10
119357

Graph is given for the equation \({y}~=~3^{{x}} \)

a) What is the \(y\)-intercept of the graph?
b) Find the value of \(y\), when \(x = 3\).
c) What happens to the graph as \(x\) increases?

a) \(y=1\)

b) \(27\)

c) \(y\) increases