Write Exponential Transformations
Understanding the Function
Exponential
Transformations
Transformations
Graphs
Tables
100
y=2x
Write an equation that has a horizontal shift of 5 units to the right.
What is y=2(x-5)?
100
Exponential functions are growth functions when which variable is greater than 1?
hint: recall the equation y=a(b)x
b (The common ratio)
100
This is the formula for exponential transformations
What is y = -a(b)(x-h) +K
100
Is this exponential growth or decay?
What is exponential decay.
100
What model does this table represent? Linear or exponential?
-1 Linear
200
y=5x
write an equation with a vertical shift of 8 units down
What is y=5x -8?
200
Consider the function below? What is the percent decrease?
f(x)=150(0.98)x
2%
200
This is what the "a" and "b" values are in a(b)x.
What is the stretch-shrink factor and growth-decay?
200
Is this exponential growth or decay?
What is exponential growth.
200
Linear or Exponential?
Exponential x2
300
y=2x
Write an equation with a vertical shift of 3 units down and a reflection across the x-axis.
What is y=-2x -3
300
What is the variable in an exponential function that represents the initial value of whatever is being measured for modeling problems.
hint: recall the equation a(b)x
a
300
True or false: In the equation, y= 2(x-5) +6, the transformation includes a shift to the right 5 units.
What is True there is h value of -5 meaning a shift of 5 to the right.
300
What is the b in the function graphed for the model f(x)=a(b)x?
4
300
Linear or Exponential?
Exponential divide by 4
400
y=(2)x
write an equation with a horizontal shift of 6 units down, a stretch of 2, and a reflection across the x-axis.
What is y=-2(2)(x-6)?
400
The variable b in an exponential function can be called_______.
hint: recall y=a(b)x
Base, common ratio, multiplier, (Growth/Decay) factor
400
Describe transformations f(x) = 10(5)(x+8)
What is a stretch by a factor of 10, growth function and a horizontal shift of 8 units to the left?
400
f(x)=4x
g(x)=4x+k
If the function moved down 2 units, What is k?
-2
400
Linear or Exponential?
Exponential x6
500
y=(4)x
Write an equation with a horizontal shift of 7 units down, and a shrink of 1/2
what is y=1/2(4)(x-7)
500
consider the function below. What is the percent increase?
f(x)=200(1.05)x
5%
500
y=-(1.02)(x-3) +10
Explain transformations! Hint- You should have 4 total transformations.
What is a reflection, growth function, horizontal shift right 3 units and vertical shift up 10 units.
500
We we started with f(x)=2(0.50)x (Red)
g(x)=2(0.50)x (Blue) Find k
-3
500
Linear or exponential?
x y
5 34.5
6 40.5
7 46.5
8 52.5
9 58.5
Linear +6