EXPONENTIAL FUNCTION: 𝒚 = 𝒃𝒙
LOGARITHMIC FUNCTION: 𝒚 = 𝐥𝐨𝐠 𝒃 𝒙
DOMAIN:
DOMAIN:
RANGE:
RANGE:
HA:
VA:
ANCHOR POINTS:
ANCHOR POINTS:
0<𝑏<1
0<𝑏<1
1 𝑥
Graph: 𝑦 = (2)
Graph: 𝑦 = log 1 𝑥
𝑏>1
𝑏 >1
Graph: 𝑦 = 2𝑥
Graph: 𝑦 = log 2 𝑥
2
0 < 𝑏 <1
𝑏>1
Exponential and Logarithmic Functions:
1. Inverses of one another: One function undoes the other. Domain (𝑥 values) and range (𝑦 values) are switched. The inverse of 𝑓(𝑥) is 𝑓 −1 (𝑥)
𝑓(𝑥) = 2𝑥
x
-1
0
1
𝑓 −1 (𝑥 ) = log 2 𝑥
y
½
1
2
x
y
½
1
2
-1
0
1
2. Both are one-to-one functions: Each element of the range is matched to exactly one element in the domain. (outputs or 𝑦 values never repeat)
The Horizontal Line Test can tell you if a graph is one-to-one. The horzontal line only crosses through the function at one point.
3. Reflect in the line: 𝑦 = 𝑥