help with transformations of exponenetial function

[yfelix45]

Describe the transformations that must be applied to the graph of y = 5^x to obtain the graph of y = 2 - 3 (5^x+ 4). I have done transformations of exponential functions which have been transformed. How can I do this with the information given?

Thanks

 

[srmichael]

Describe the transformations that must be applied to the graph of y = 5^x to obtain the graph of y = 2 - 3 (5^x+ 4). I have done transformations of exponential functions which have been transformed. How can I do this with the information given?

Thanks

You might want to first start by noticing that \(\displaystyle y=2-3(5^x+4)\) equals \(\displaystyle y=-3\cdot5^x - 10\). Can you take it from here?

 

[Deleted member 4993]

Describe the transformations that must be applied to the graph of y = 5^x to obtain the graph of y = 2 - 3 (5^x+ 4). I have done transformations of exponential functions which have been transformed. How can I do this with the information given?

Thanks

Another way to think would be:

\(\displaystyle y_3 = 5^x \ \to \ y_2 = 5^x + 4 \ \to \ y_1 = -3(5^x + 4) \ \ \to \ y = 2 - 3(5^x + 4)\)

 

[srmichael]

Another way to think would be:

\(\displaystyle y_3 = 5^x \ \to \ y_2 = 5^x + 4 \ \to \ y_1 = -3(5^x + 4) \ \ \to \ y = 2 - 3(5^x + 4)\)

Yup...more than one way to skin a cat.

 

[soroban]

Hello, yfelix45!

\(\displaystyle \text{Describe the transformation that must be applied to the graph of }\,y\,=\,5^x\)
\(\displaystyle \text{to obtain the graph of }\, y \:=\: 2 - 3 (5^x+ 4)\)

We know the graph of \(\displaystyle y \,=\,5^x\)

The graph of \(\displaystyle y \:=\:5^x + 4\) is moved up 4 units.

The graph of \(\displaystyle y \:=\:3(5^x+4)\) is magnified vertically by a factor of 3.

The graph of \(\displaystyle y \:=\:-3(5^x+4)\) is reflected over the x-axis.

The graph of \(\displaystyle y \:=\:-3(5^x+4) + 2\) is moved up 2 units.

 

[yfelix45]

Thanks

hello,

Thanks for the help.

yihan