Question

3. 23F Given a function h(x) and (&)-e -3) + 6. Describe how to get the graph of k(i) from the graph of h(x). Be very precise about the order of the transformation and the unit of each transformation. 4. 24T Convert the angle 215° to radian. (Keep your answer exact and do not round it to decimals.)

Answer 1

3 . Here we have our function $h(x)=e^x$ . And this get transformed into  $k(x)=e^{-8(x-3)}+6$

So the order of transformations are ;

• $h(x)\rightarrow h(x-3)$ , there is a horizontal shift of 3 units to the right .
• $h(x-3)\rightarrow h(8(x-3))$ , there is a horizontal shrink of 8 units to the shifted graph.
• $h(8(x-3))\rightarrow h(-8(x-3))$ , the graph gets reflected about y axis .
• $h(-8(x-3))\rightarrow h(-8(x-3))+6$ , the graph gets a vertical upward shift of 6 units

By doing these transformation we get the function k(x) from h(x).

4 . A 180° angle is equivalent to $\pi$ radians . So to convert 215° to radians , we get

$215*\frac{\pi}{180}=\frac{43\pi}{36}$

We get ,

${\color{DarkRed} \frac{43\pi}{36}\ radians}$​​​​​​​