Math  /  Algebra

Question(a) Is f(1)f(1) negative? Yes No (b) For which value(s) of xx is f(x)>0f(x)>0 ?
Write your answer using interval notation. \square (c) For which value(s) of xx is f(x)=0f(x)=0 ?
If there is more than one value, separate them with commas. \square

Studdy Solution

STEP 1

What is this asking? We're looking at a graph and figuring out where the function is positive, negative, and zero! Watch out! Don't mix up the *x*-values and *y*-values!
We're looking at the *x*-axis to figure out what makes f(x)f(x) positive, negative, or zero.

STEP 2

1. Check f(1)f(1)
2. Find where f(x)>0f(x) > 0
3. Find where f(x)=0f(x) = 0

STEP 3

Find where x=1x = 1 is on the horizontal axis.
It's **one unit** to the right of zero.

STEP 4

Look straight up from x=1x = 1 to where it hits the graph.
The *y*-value there is f(1)f(1).

STEP 5

Since the graph is **above** the *x*-axis at x=1x = 1, f(1)f(1) is **positive**.
So the answer is **No**.

STEP 6

The graph is above the *x*-axis between roughly x=3.5x = -3.5 and x=0x = 0, and then again between roughly x=0x = 0 and x=4x = 4.

STEP 7

We use parentheses because the question asks for where f(x)f(x) is *greater than* zero, not equal to zero.
So, the intervals are (3.5,0)(-3.5, 0) and (0,4)(0, 4).

STEP 8

Since the function is positive in both intervals, we combine them with the union symbol: (3.5,0)(0,4)(-3.5, 0) \cup (0, 4).

STEP 9

The graph crosses the *x*-axis at approximately x=3.5x = -3.5, x=0x = 0, and x=4x = 4.

STEP 10

The *x*-values where f(x)=0f(x) = 0 are 3.5-3.5, 00, and 44.

STEP 11

(a) No (b) (3.5,0)(0,4)(-3.5, 0) \cup (0, 4) (c) 3.5,0,4-3.5, 0, 4

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