The graph of y = 2^x-3 can be obtained by shifting the graph of y= 2^x

a) 3 units to the right
b) 3 units to the left
c) 3 units up
d) 3 units down
e) 2 units to the right and 3 units up

The equation of the graph that is obtained by reflecting the graph of y = 3^-x in the y axis is

a) y =-3^x
b) y=(1/3)^x
c) y= -(1/3)^x
d) y= 3^x
e) x= 3^y

a) 3 units to the right. Because shifting the graph of y = 2^x-3 three units to the right would result in the equation y = 2^(x-3).

For the first question, the graph of y = 2^x can be shifted by adding or subtracting constants to obtain the graph of y = 2^x - 3. Let's go through each option to see which one is correct:

a) Shifting 3 units to the right means adding 3 to x. So, the equation would be y = 2^(x-3). This is not the correct option.

b) Shifting 3 units to the left means subtracting 3 from x. So, the equation would be y = 2^(x+3). This is not the correct option.

c) Shifting 3 units up means adding 3 to y. So, the equation would be y + 3 = 2^x. This is not the correct option.

d) Shifting 3 units down means subtracting 3 from y. So, the equation would be y - 3 = 2^x. This is the correct option.

e) Shifting 2 units to the right and 3 units up means adding 2 to x and adding 3 to y. So, the equation would be (y + 3) = 2^(x + 2). This is not the correct option.

Therefore, the correct answer is d) 3 units down.

For the second question, reflecting the graph of y = 3^(-x) in the y-axis means changing the sign of x. So, the equation would be y = 3^(-x).

Therefore, the correct answer is a) y = -3^x.

To obtain the graph of y = 2^x-3 by shifting the graph of y = 2^x, we need to consider the effects of the given equation y = 2^x-3.

Looking at the equation y = 2^x-3, we can see that the graph is shifted down by 3 units because of the "-3" term. This means that each y-coordinate of the graph is reduced by 3 units compared to the original graph of y = 2^x.

Hence, the correct option for shifting the graph of y = 2^x to obtain the graph of y = 2^x-3 is (d) 3 units down.

Now, let's consider the equation that reflects the graph of y = 3^-x in the y-axis.

A reflection in the y-axis simply means that the x-coordinates of the graph are negated. So, for the graph of y = 3^-x, we need to negate the x-coordinates.

The correct option for the equation that reflects the graph of y = 3^-x in the y-axis is (b) y = (1/3)^x.

In this equation, when x is positive, the exponent (1/x) results in a fraction less than 1. When x is negative, the exponent (-1/x) results in a fraction greater than 1. This reflects the behavior of the graph of y = 3^-x.

Note: Option (a) y = -3^x is incorrect because it doesn't represent the reflection in the y-axis.

(D)

(D)