1a. Graph f(x)=2^x+1 . Label three points. x & y & & & a Domain b Range c Asymptote:

To graph \( f(x) = 2^x + 1 \), we can choose three points by substituting different values of \( x \):<br /><br />1. When \( x = -1 \):<br />\[ f(-1) = 2^{-1} + 1 = \frac{1}{2} + 1 = 1.5 \]<br />So, one point is \((-1, 1.5)\).<br /><br />2. When \( x = 0 \):<br />\[ f(0) = 2^0 + 1 = 1 + 1 = 2 \]<br />So, another point is \((0, 2)\).<br /><br />3. When \( x = 1 \):<br />\[ f(1) = 2^1 + 1 = 2 + 1 = 3 \]<br />So, the third point is \((1, 3)\).<br /><br />These points are:<br />\[<br />\begin{array}{c}<br />(-1, 1.5) \\<br />(0, 2) \\<br />(1, 3) \\<br />\end{array}<br />\]<br /><br />a. Domain: The domain of \( f(x) = 2^x + 1 \) is all real numbers.<br />\[ \text{Domain: } (-\infty, \infty) \]<br /><br />b. Range: Since \( 2^x \) is always positive and adding 1 shifts it up by 1 unit, the range is all values greater than 1.<br />\[ \text{Range: } (1, \infty) \]<br /><br />c. Asymptote: The horizontal asymptote is the line that the function approaches as \( x \) goes to negative infinity. For \( f(x) = 2^x + 1 \), the horizontal asymptote is \( y = 1 \).<br />\[ \text{Asymptote: } y = 1 \]