To solve this problem, we need to interpret the graph of the function $ f(x) $. The graph is plotted on a coordinate grid where each square represents 1 unit. We will find the requested values by locating points on the graph.
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a. $ f(-4) $
We want the value of the function when $ x = -4 $. Locate $ x = -4 $ on the x-axis (4 units left of the origin). Move vertically up to the curve. From the graph, the point $ (-4, 3) $ lies on the curve.
✔ So, $ f(-4) = 3 $
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b. $ f(0) $
Locate $ x = 0 $ (the y-axis). Move vertically to the curve. The graph passes through the origin $ (0, 0) $.
✔ So, $ f(0) = 0 $
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c. $ f(3) $
Locate $ x = 3 $ on the x-axis (3 units right of the origin). Move vertically to the curve. The point $ (3, -2) $ lies on the curve.
✔ So, $ f(3) = -2 $
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d. $ f(-5) $
Locate $ x = -5 $ on the x-axis (far left end). Move vertically to the curve. The point $ (-5, 0) $ lies on the curve.
✔ So, $ f(-5) = 0 $
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e. $ x $ when $ f(x) = 2 $
We now look for all x-values where the
y-value is 2. Draw a horizontal line at $ y = 2 $ and see where it intersects the graph.
Looking at the graph:
- On the left side (negative x), the curve reaches y=2 at approximately $ x = -3 $
- On the right side (positive x), the curve rises again and hits y=2 at approximately $ x = 4 $
✔ So, the solutions are $ x = -3 $ and $ x = 4 $
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f. $ x $ when $ f(x) = 0 $
This means finding the
x-intercepts — where the graph crosses or touches the x-axis (y=0).
From the graph:
- At $ x = -5 $, the graph touches the x-axis.
- At $ x = 0 $, the graph passes through the origin.
- At $ x = 5 $, the graph ends on the x-axis.
✔ So, the solutions are $ x = -5 $, $ x = 0 $, and $ x = 5 $
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✔ Final Answers:
a. $ f(-4) = 3 $
b. $ f(0) = 0 $
c. $ f(3) = -2 $
d. $ f(-5) = 0 $
e. $ x = -3 $ and $ x = 4 $
f. $ x = -5 $, $ x = 0 $, and $ x = 5 $
Parent Tip: Review the logic above to help your child master the concept of function notation worksheet with answers.
