Answered

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Jamelia observes that if [tex]$f(x) = 2$[/tex], then the graphs of [tex]$4f(x)$[/tex] and [tex][tex]$f(x) + 3$[/tex][/tex] both have a y-intercept of 1.

Does this mean that multiplying [tex]$f(x)$[/tex] by 4 and adding 3 to [tex]$f(x)$[/tex] transform the graph in the same way?

A. Yes. They transform the point [tex][tex]$(0, f(0))$[/tex][/tex] in the same way, so they will transform all other points in the same way.
B. No. They transform the point [tex]$(0, f(0))$[/tex] in the same way but not the other points on the graph.
C. Yes. All exponential graphs look the same and have the same shape.
D. No. Jamelia is incorrect because the y-intercept of [tex]$4f(x)$[/tex] is 4 and the y-intercept of [tex][tex]$f(x) + 3$[/tex][/tex] is 3.

Sagot :

GinnyAnswer
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.
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