Evaluating Functions From A Graph Practice worksheet with four function graphs and related questions.

Let’s solve each part step by step. We’ll look at each graph and find the values asked.

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Top Left Graph (first one):

We need to find:
1. f(3) = ?
2. If f(x) = -3, what is x?

Looking at the first graph: it’s a straight line going through the origin (0,0), and for every 1 unit right, it goes up 1 unit — so slope is 1. That means f(x) = x.

So:
- f(3) = 3 → because when x=3, y=3 on the line.
- If f(x) = -3, then x = -3 → because when y=-3, x must be -3.

✔ Check: On the graph, point (3,3) is on the line. Point (-3,-3) is also on the line. Correct.

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Top Right Graph (second one):

This is a V-shaped graph (absolute value type), but flipped upside down? Wait — actually, it peaks at (0,3), and goes down to left and right.

Points we can see:
- At x=0, y=3 → vertex
- At x=1, y=2
- At x=2, y=1
- At x=-1, y=2
- At x=-2, y=1

So it looks like f(x) = 3 - |x|

Check:
- f(2) = 3 - |2| = 1 → yes, matches graph.
- Now, if f(x) = 3, then 3 - |x| = 3 → |x| = 0 → x = 0

✔ So:
- f(2) = 1
- f(x)=3 → x=0

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Bottom Left Graph (third one):

This graph has three parts:
- From left: starts low, rises to (-3,2), then flat until x=0, then rises again.

Specifically:
- For x ≤ -3: line from (-4,0) to (-3,2) → slope = (2-0)/(-3+4) = 2/1 = 2 → equation: y - 0 = 2(x + 4) → y = 2x + 8
Wait — let’s check with points:
At x=-4, y=0 → 2*(-4)+8 = 0 ✔️
At x=-3, y=2 → 2*(-3)+8 = 2 ✔️

Then from x=-3 to x=0: horizontal line at y=2.

Then from x=0 onward: line from (0,2) to (1,4) → slope = (4-2)/(1-0) = 2 → y = 2x + 2

Now answer questions:

1. f(-1) = ? → since -1 is between -3 and 0, it’s on the flat part → y=2 → so f(-1)=2

2. f(x) = -2 → where does y=-2?

Look at the left part: y = 2x + 8. Set equal to -2:

2x + 8 = -2
2x = -10
x = -5

Check: at x=-5, y=2*(-5)+8 = -10+8 = -2 ✔️

Is there any other place? The middle part is y=2, right part is y≥2 → no. Only x=-5.

✔ So:
- f(-1) = 2
- f(x)=-2 → x=-5

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Bottom Right Graph (fourth one):

This is a curve — looks like a cubic or something similar.

We need:
1. f(0) = ?
2. If f(x)=5, what is x?

Look at graph:
- At x=0, the graph crosses y-axis at y=2 → so f(0)=2

Now, f(x)=5 → where does the graph reach y=5?

Looking at the peak: it goes up to about y=5 at x=2? Let’s check:

The highest point seems to be at x=2, y=5 → yes, that’s the top of the hill.

Is there another point? On the left side, as x goes negative, it goes down to y=-3 around x=-3, then comes back up — but never reaches 5 again. Only at x=2.

Wait — let me double-check: at x=2, y=5? Yes, the graph shows the peak at (2,5).

So:
- f(0) = 2
- f(x)=5 → x=2

✔ Confirmed.

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Final Answers:

Top Left:
f(3) = 3
f(x) = -3 → x = -3

Top Right:
f(2) = 1
f(x) = 3 → x = 0

Bottom Left:
f(-1) = 2
f(x) = -2 → x = -5

Bottom Right:
f(0) = 2
f(x) = 5 → x = 2

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Final Answer:
f(3) = 3; x = -3
f(2) = 1; x = 0
f(-1) = 2; x = -5
f(0) = 2; x = 2