MCR3U1
U6L4
EXPLORING THE PROPERTIES OF EXPONENTIAL FUNCTIONS
(An Investigation)
PART A ~ DEFINITION
An exponential function is a function of the form: 𝑦 = 𝑎(𝑏)𝑥
PART B ~ GRAPHING EXPONENTIAL FUNCTIONS
Graph the exponential functions, 𝑦 = 2𝑥 and 𝑦 = 2−𝑥 , on the given grid.
y
x
𝑦=2
𝑥
–3
–2
–1
0
1
2
3
x
1 𝑥
𝑦=( )
2
–3
–2
–1
0
1
2
3
x
PART C ~ PROPERTIES OF EXPONENTIAL FUNCTIONS
PROPERTIES
𝑦 = 2𝑥
1 𝑥
𝑦 = 2−𝑥 or 𝑦 = (2)
domain
range
y–intercept
equation of the asymptote
increasing/decreasing
function
The exponential function, 𝑦 = 𝑏 𝑥 , is:
 an increasing function representing growth when b > 1
 an decreasing function representing decay when 0 < b < 1
MCR3U1
U6L4
PART D ~ COMPARING FIRST DIFFERENCES OF VARIOUS FUNCTIONS
Linear, quadratic, and exponential functions have unique first–difference patterns
that allow them to be recognized.
Calculate the first–differences for each of the following functions:
Function:
LINEAR
x
1
2
3
4
5
QUADRATIC
𝑦 = 2𝑥
x
1
2
3
4
5
EXPONENTIAL
𝑦 = 𝑥2
𝑦 = 2𝑥
x
1
2
3
4
5
Patterns Observed in the First–differences:
Sketch each of the following functions on the same set of axes:
y
 𝑦 = 3𝑥 , 𝑦 = 4𝑥 , 𝑦 = 5𝑥
 𝑦 = 1𝑥
1 𝑥
1 𝑥
1 𝑥
 𝑦=( ) , 𝑦=( ) , 𝑦=( )
3
4
5
Why do all exponential graphs
share a POI of (0, 1)?
1
x
HOMEWORK: p.243 #1, 2