Graphing Exponential Functions Investigation
How do parameters affect exponential functions?
y = a•2
æ x-h ö
ç
÷
è b ø
+k
For each function, identify (a) if the function is growth or decay, (b) the domain, (c) the range, and
(d) equation of the asymptote. Graph the function, labeling at least 3 points.
Graph the following exponential functions using DESMOS. Each is a transformation of the graph of y = 2x. As
you graph, take note of the impact of the a, h, b, and k on the function.
1) y = 2x
(a)___________________
(b)___________________
(c)___________________
(d)___________________
2) y = 2x + 3
(a)___________________
(b)___________________
(c)___________________
(d)___________________
3) y = 2x – 1
(a)___________________
(b)___________________
(c)___________________
(d)___________________
Describe the effect of ‘k’ on the parent function y = 2x.
4) y = 2x+5
(a)___________________
(b)___________________
(c)___________________
(d)___________________
5) y = 2x – 3
(a)___________________
(b)___________________
(c)___________________
(d)___________________
6) y = 2x + 3
(a)___________________
(b)___________________
(c)___________________
(d)___________________
Describe the effect of ‘h’ on the parent function y = 2x.
Using your knowledge of transformation of functions, how will ‘a’ and ‘b’ affect the graph of the parent
function y = 2x.
7) y = –2x
(a)___________________
(b)___________________
(c)___________________
(d)___________________
8) y = 2–x
(a)___________________
(b)___________________
(c)___________________
(d)___________________
9) y = –2–x
(a)___________________
(b)___________________
(c)___________________
(d)___________________
Describe the effect of ‘a’ and ‘b’ on the graph of the parent function y = 2x.