One more question:
Beginning with the function f(x) = (0.8)^(x), state what transformations were used on this to obtain the functions given below.
a) g(x) = - (0.8)^(x) - 2
b) h(x) = (1/2) (0.8)^(x-2)
c) k(x) = (0.8)^(-3x+9)
These are the answers I have, (may be incorrect)
a) reflect across the horizontal axis
moved down by 2 units
b) moved right by 2 units
vertically compressed by (1/2)
c) reflect across the vertical axis
moved left by 9 units
horizontal compression by 3
Thanks.
in c) I object to your horizontal movement
k(x) = (.8)^(-3x+9)
= (.8)^( -3(x-3) )
so moved to the right by 3 units
Thanks, glad I can correct that!
Great effort on providing the answers! Here's a breakdown of the transformations for each function:
a) For g(x) = -(0.8)^(x) - 2:
- Reflection across the horizontal axis: The negative sign in front of the function, -(0.8)^(x), reflects the graph vertically across the x-axis.
- Translation downward by 2 units: The "- 2" term at the end of the function shifts the graph vertically downward by 2 units.
So, your answer for function g(x) is correct.
b) For h(x) = (1/2)(0.8)^(x-2):
- Translation right by 2 units: The "(x - 2)" inside the exponent of the function moves the graph horizontally to the right by 2 units.
- Vertical compression by a factor of (1/2): The (1/2) coefficient in front of the function compresses the graph vertically by a factor of 1/2, making it steeper.
So, your answer for function h(x) is correct as well.
c) For k(x) = (0.8)^(-3x + 9):
- Reflection across the vertical axis: The negative coefficient of the exponent, (-3x + 9), reflects the graph horizontally across the y-axis.
- Translation left by 9 units: The "+ 9" at the end of the exponent moves the graph horizontally to the left by 9 units.
- Horizontal compression by a factor of 3: The coefficient of the x-variable, -3, compresses the graph horizontally by a factor of 3, making it narrower.
So, based on the transformations described, your answer for function k(x) is correct too.
Well done!