Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To determine how the graph of [tex]\( g(x) = f(x + 8) + 4 \)[/tex] compares with the graph of [tex]\( f(x) \)[/tex], let's break down the transformation step by step.
1. Horizontal Shift:
- The argument of the function [tex]\( f \)[/tex] is [tex]\( x + 8 \)[/tex]. Adding a positive constant inside the function argument results in a horizontal shift to the left.
- Specifically, [tex]\( f(x + 8) \)[/tex] means the function [tex]\( f(x) \)[/tex] is shifted 8 units to the left on the x-axis.
2. Vertical Shift:
- The entire functional value [tex]\( f(x + 8) \)[/tex] is then increased by 4.
- Adding a positive constant outside the function results in a vertical shift upward.
- Thus, [tex]\( f(x + 8) + 4 \)[/tex] means the function is shifted 4 units up on the y-axis.
Combining these transformations:
- The graph of [tex]\( g(x) \)[/tex] is the graph of [tex]\( f(x) \)[/tex] shifted 8 units to the left and 4 units up.
Thus, the best statement that describes this transformation is:
B. The graph of [tex]\( g(x) \)[/tex] is the graph of [tex]\( f(x) \)[/tex] shifted 8 units to the left and 4 units up.
1. Horizontal Shift:
- The argument of the function [tex]\( f \)[/tex] is [tex]\( x + 8 \)[/tex]. Adding a positive constant inside the function argument results in a horizontal shift to the left.
- Specifically, [tex]\( f(x + 8) \)[/tex] means the function [tex]\( f(x) \)[/tex] is shifted 8 units to the left on the x-axis.
2. Vertical Shift:
- The entire functional value [tex]\( f(x + 8) \)[/tex] is then increased by 4.
- Adding a positive constant outside the function results in a vertical shift upward.
- Thus, [tex]\( f(x + 8) + 4 \)[/tex] means the function is shifted 4 units up on the y-axis.
Combining these transformations:
- The graph of [tex]\( g(x) \)[/tex] is the graph of [tex]\( f(x) \)[/tex] shifted 8 units to the left and 4 units up.
Thus, the best statement that describes this transformation is:
B. The graph of [tex]\( g(x) \)[/tex] is the graph of [tex]\( f(x) \)[/tex] shifted 8 units to the left and 4 units up.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.