To determine if multiplying [tex]\( f(x) \)[/tex] by 4 and adding 3 to [tex]\( f(x) \)[/tex] transform the graph in the same way, let's analyze the transformations step by step. We are given:
[tex]\[ f(x) = 2 \][/tex]
Let's first compute the y-intercepts for the transformed functions.
1. For [tex]\( 4f(x) \)[/tex]:
[tex]\[ f(x) = 2 \][/tex]
[tex]\[ 4f(x) = 4 \cdot 2 = 8 \][/tex]
So, the y-intercept of [tex]\( 4f(x) \)[/tex] is 8.
2. For [tex]\( f(x) + 3 \)[/tex]:
[tex]\[ f(x) = 2 \][/tex]
[tex]\[ f(x) + 3 = 2 + 3 = 5 \][/tex]
So, the y-intercept of [tex]\( f(x) + 3 \)[/tex] is 5.
Now, comparing the results:
- The y-intercept of [tex]\( 4f(x) \)[/tex] is 8.
- The y-intercept of [tex]\( f(x) + 3 \)[/tex] is 5.
From this, we can conclude that the y-intercepts are different. Therefore, multiplying [tex]\( f(x) \)[/tex] by 4 and adding 3 to [tex]\( f(x) \)[/tex] do not transform the graph in the same way.
Thus, Jamelia's assertion that if [tex]\( f(x) = 2 \)[/tex], then the graphs of [tex]\( 4f(x) \)[/tex] and [tex]\( f(x) + 3 \)[/tex] both have a y-intercept of 1 is incorrect. The correct choice is:
No. Jamelia is incorrect because the y-intercept of [tex]\( 4f(x) \)[/tex] is 8 and the y-intercept of [tex]\( f(x) + 3 \)[/tex] is 5.
