Answered

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The point [tex]\((-3, -5)\)[/tex] is on the graph of a function. Which equation must be true regarding the function?

A. [tex]\(f(-3) = -5\)[/tex]
B. [tex]\(f(-3, -5) = -8\)[/tex]
C. [tex]\(f(-5) = -3\)[/tex]
D. [tex]\(f(-5, -3) = -2\)[/tex]

Sagot :

GinnyAnswer
Let's consider the point [tex]\((-3, -5)\)[/tex] on the graph of the function. This point informs us about the behavior of the function at [tex]\( x = -3 \)[/tex]. The notation [tex]\( (-3, -5) \)[/tex] means that when [tex]\( x = -3 \)[/tex], the function [tex]\( f \)[/tex] maps [tex]\( x \)[/tex] to [tex]\( y = -5 \)[/tex]. Hence, this indicates that [tex]\( f(-3) = -5 \)[/tex].

Now let's analyze each given equation to determine which one is true:

1. [tex]\( f(-3) = -5 \)[/tex]:
- This is our candidate, as it directly states the behavior we've identified: when [tex]\( x = -3 \)[/tex], the function outputs [tex]\( -5 \)[/tex].

2. [tex]\( f(-3, -5) = -8 \)[/tex]:
- This form is not typically used for functions that map a single [tex]\( x \)[/tex] to a single [tex]\( y \)[/tex]. This notation suggests a function of two variables, which is not the case here.

3. [tex]\( f(-5) = -3 \)[/tex]:
- This would imply that when [tex]\( x = -5 \)[/tex], the function outputs [tex]\( -3 \)[/tex]. However, our given information only tells us about the point [tex]\((-3, -5)\)[/tex], not about [tex]\( f(-5) \)[/tex].

4. [tex]\( f(-5, -3) = -2 \)[/tex]:
- Similar to the second option, this suggests a function of two variables. Additionally, the values [tex]\((-5, -3)\)[/tex] are not relevant to our given point.

Thus, the only equation that must be true considering the point [tex]\((-3, -5)\)[/tex] is:

[tex]\[ f(-3) = -5 \][/tex]

So, the correct choice is the first one.
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