the graph of a function f(x) passes through the following points:

Question

the graph of a function f(x) passes through the following points:
(0,-2),(1,0),(-1,-4)
which of the following could be f(x)?
a)f(x)=2x-2
b)f(x)=2x^2-2
c)f(x)=-2x-2
d)f(x)=2√x-2

GPT-4o mini · Answer

To determine which function $ f(x) $ passes through the points $(0, -2)$, $(1, 0)$, and $(-1, -4)$, we can evaluate each of the provided options at these specific $ x $ values. ### a) $ f(x) = 2x - 2 $ - For $ x = 0 $: $$ f(0) = 2(0) - 2 = -2 \quad \text{(matches)} $$ - For $ x = 1 $: $$ f(1) = 2(1) - 2 = 0 \quad \text{(matches)} $$ - For $ x = -1 $: $$ f(-1) = 2(-1) - 2 = -2 - 2 = -4 \quad \text{(matches)} $$ This function matches all three points. ### b) $ f(x) = 2x^2 - 2 $ - For $ x = 0 $: $$ f(0) = 2(0)^2 - 2 = -2 \quad \text{(matches)} $$ - For $ x = 1 $: $$ f(1) = 2(1)^2 - 2 = 2 - 2 = 0 \quad \text{(matches)} $$ - For $ x = -1 $: $$ f(-1) = 2(-1)^2 - 2 = 2 - 2 = 0 \quad \text{(does NOT match)} $$ This function does NOT match all three points. ### c) $ f(x) = -2x - 2 $ - For $ x = 0 $: $$ f(0) = -2(0) - 2 = -2 \quad \text{(matches)} $$ - For $ x = 1 $: $$ f(1) = -2(1) - 2 = -2 - 2 = -4 \quad \text{(does NOT match)} $$ - For $ x = -1 $: $$ f(-1) = -2(-1) - 2 = 2 - 2 = 0 \quad \text{(does NOT match)} $$ This function does NOT match all three points. ### d) $ f(x) = 2\sqrt{x} - 2 $ - For $ x = 0 $: $$ f(0) = 2\sqrt{0} - 2 = -2 \quad \text{(matches)} $$ - For $ x = 1 $: $$ f(1) = 2\sqrt{1} - 2 = 2 - 2 = 0 \quad \text{(matches)} $$ - For $ x = -1 $: $$ f(-1) \quad \text{(undefined as you can't take the square root of a negative number)} $$ This function does NOT match all three points. ### Conclusion The only function that matches all three points is: **a)** $ f(x) = 2x - 2 $

the graph of a function f(x) passes through the following points:

a) \( f(x) = 2x - 2 \)

b) \( f(x) = 2x^2 - 2 \)

c) \( f(x) = -2x - 2 \)

d) \( f(x) = 2\sqrt{x} - 2 \)

Conclusion