Question

1. convert: $\frac{11pi}{30}$ into degrees. $\frac{11pi}{30}cdot\frac{180}{pi}$ 10. graph $y = 2^{x - 3}+1$.

Explanation:

Step1: Recall conversion formula

We know that to convert radians to degrees, we use the formula $\text{Degrees}=\text{Radians}\times\frac{180^{\circ}}{\pi}$. Given $\text{Radians}=\frac{11\pi}{30}$, we substitute it into the formula: $\frac{11\pi}{30}\times\frac{180^{\circ}}{\pi}$.

Step2: Simplify the expression

The $\pi$ in the numerator and denominator cancels out. Then, $\frac{11}{30}\times180 = 11\times6=66$. So the angle in degrees is $66^{\circ}$.

Step3: Analyze the exponential - function for graphing

For the function $y = 2^{x - 3}+1$, first consider the parent - function $y = 2^{x}$. The transformation $y = 2^{x - 3}$ is a horizontal shift of the parent - function $y = 2^{x}$ to the right by 3 units. The transformation $y = 2^{x - 3}+1$ is a vertical shift of $y = 2^{x - 3}$ up by 1 unit.

Step4: Find key points

When $x = 3$, $y=2^{3 - 3}+1=2^{0}+1=1 + 1=2$. As $x\to-\infty$, $y = 2^{x - 3}+1\to1$ (since $2^{x - 3}\to0$ as $x\to-\infty$). We can also find other points by choosing values of $x$, for example, when $x = 4$, $y=2^{4 - 3}+1=2 + 1=3$.

Answer:

1. The angle $\frac{11\pi}{30}$ in degrees is $66^{\circ}$.
2. To graph $y = 2^{x - 3}+1$:

• The horizontal asymptote is $y = 1$.
• The point $(3,2)$ lies on the graph.
• As $x$ increases, the function is an exponential growth function shifted 3 units to the right and 1 unit up from the parent - function $y = 2^{x}$.