Warm Up Solutions

Name the domain and range of the function in interval notation.

$y = 2^{x - 8} + 5$

Domain: $(- \infty, + \infty)$
Range: $(5, + \infty)$

$y = 3^{5 - x} - 3$

Domain: $(- \infty, + \infty)$
Range: $(- 3, + \infty)$

Note

Q: What are the asymptotes for problems 1 and 2?
A: problem 1: $y = 5$ , problem 2: $y = - 3$

Name the end behavior.

$x \to - \infty, f (x) \to - 3, and x \to + \infty, f (x) \to + \infty$

$x \to - 2, f (x) \to - 3, and x \to + \infty, f (x) \to + \infty$

Note

Q: What are the similarities and differences between the end behaviors?
A: Both continue toward positive infinity for x and f(x). The difference is that x approaches negative infinity in problem 3 and x approaches –2 in problem 4.