3) Describe the transformation from f(x) to g(x).
f(x)=4^x to g(x)=5*4^-x+3
A. Reflect across the x-axis and up 3 units
B. Right 3 units, vertical stretch by a factor of 3, and reflect across the y-axis
C. Right 5 units and horizontal stretch by a factor of 4
D. Vertical stretch by a factor of 5, reflect across the y-axis, and up 3 units
9) Describe the transformation from f(x) to g(x).
f(x)=log x to g(x)=-log x -5
A. Reflect across the x-axis and down 5 units
B. Right 5 units and reflect across the y-axis
C. Vertical stretch by a factor of 1 and down 5 units
D. Left 1 unit and reflect across the x-axis
please help
I can't, there's to much to look at and decipher 😟❓
<3
3) clearly D
9) A
To describe the transformation from f(x) to g(x), we need to compare the equations of f(x) and g(x) and identify the changes that have been made. Let's analyze each option for both parts of the question.
3) Describe the transformation from f(x) = 4^x to g(x) = 5 * 4^-x + 3.
A. Reflect across the x-axis and up 3 units: This option involves both a reflection across the x-axis and a vertical shift upwards but does not address the change in the base of the exponent.
B. Right 3 units, vertical stretch by a factor of 3, and reflect across the y-axis: This option does not account for the change in the base of the exponent.
C. Right 5 units and horizontal stretch by a factor of 4: This option involves a horizontal shift and a horizontal stretch, but does not consider the change in the base of the exponent.
D. Vertical stretch by a factor of 5, reflect across the y-axis, and up 3 units: This option accounts for the correct changes. The factor of 5 denotes a vertical stretch, the reflection across the y-axis indicates the change in the base sign, and the upward shift of 3 units completes the transformation.
Therefore, the correct answer is D. Vertical stretch by a factor of 5, reflect across the y-axis, and up 3 units.
9) Describe the transformation from f(x) = log x to g(x) = -log x - 5.
A. Reflect across the x-axis and down 5 units: This option addresses the reflection across the x-axis but does not account for the change in sign of the logarithm.
B. Right 5 units and reflect across the y-axis: This option only involves horizontal shifting and reflection but does not consider the change in sign.
C. Vertical stretch by a factor of 1 and down 5 units: This option only includes a horizontal shift downwards but does not consider the change in sign.
D. Left 1 unit and reflect across the x-axis: This option suggests a horizontal shift to the left but does not address the change in sign.
Therefore, none of the given options accurately describe the transformation from f(x) to g(x) in this case.