chapter 1 quiz (1.1,1.2, 1.4, 1.5, 1.7)
14 points possible answered: 9/14
question 10
use the graphs to evaluate the expressions below.
$f(g(4)) = $
$g(f(2)) = $
$f(f(3)) = $
$g(g(0)) = $

Question

Accepted Answer

### For $ f(g(4)) $:
# Explanation:
## Step1: Find $ g(4) $
From the graph of $ g(x) $, when $ x = 4 $, $ g(4)=2 $.
## Step2: Find $ f(2) $
From the graph of $ f(x) $, when $ x = 2 $, $ f(2)=0 $.
# Answer:
$ f(g(4)) = 0 $

### For $ g(f(2)) $:
# Explanation:
## Step1: Find $ f(2) $
From the graph of $ f(x) $, when $ x = 2 $, $ f(2)=0 $.
## Step2: Find $ g(0) $
From the graph of $ g(x) $, when $ x = 0 $, $ g(0)=1 $. Wait, no, wait. Wait, $ f(2) = 0 $, then we need $ g(0) $? Wait, no, $ f(2) = 0 $, so $ g(f(2))=g(0) $. Wait, from $ g(x) $ graph, at $ x = 0 $, the value is 1? Wait, no, looking at the $ g(x) $ graph: the $ g(x) $ starts at (0,1)? Wait, no, the $ g(x) $ graph: when $ x = 0 $, the point is (0,1)? Wait, no, let's recheck. Wait, the $ g(x) $ graph: at $ x = 0 $, the y - value is 1? Wait, no, the $ g(x) $ graph: when $ x = 0 $, the coordinate is (0,1)? Wait, no, the $ g(x) $ graph: let's see the grid. The $ g(x) $ graph: at $ x = 0 $, the point is (0,1)? Wait, no, the first point of $ g(x) $ is (0,1)? Wait, no, the $ g(x) $ graph: when $ x = 0 $, the y - value is 1? Wait, no, maybe I made a mistake. Wait, $ f(2)=0 $, so we need to find $ g(0) $. From the $ g(x) $ graph, at $ x = 0 $, the y - coordinate is 1? Wait, no, looking at the $ g(x) $ graph: the line starts at (0,1) and goes up to (1,5), then down to (2,0), etc. Wait, no, the $ g(x) $ graph: when $ x = 0 $, the value is 1? Wait, no, the $ g(x) $ graph: at $ x = 0 $, the point is (0,1)? Wait, maybe. Then $ g(0)=1 $? Wait, no, wait, the $ g(x) $ graph: let's check the coordinates. The $ g(x) $ graph: when $ x = 0 $, the y - value is 1? Wait, the first point of $ g(x) $ is (0,1), then (1,5), (2,0), (3,4), (4,2), (5,3). So $ g(0)=1 $. Wait, but $ f(2)=0 $, so $ g(f(2))=g(0)=1 $? Wait, no, that can't be. Wait, maybe I messed up $ f(2) $. Wait, $ f(x) $ graph: at $ x = 2 $, the y - value is 0 (since the graph of $ f(x) $ has a point at (2,0)). Then $ g(0) $: from $ g(x) $ graph, at $ x = 0 $, the y - value is 1? Wait, the $ g(x) $ graph: the leftmost point is (0,1), then goes up to (1,5), down to (2,0), up to (3,4), down to (4,2), up to (5,3). So yes, $ g(0)=1 $. Wait, but maybe I made a mistake. Wait, let's re - evaluate.

Wait, no, $ f(2) = 0 $, so $ g(f(2))=g(0) $. From $ g(x) $ graph, when $ x = 0 $, $ g(0)=1 $? Wait, no, the $ g(x) $ graph: at $ x = 0 $, the y - coordinate is 1? Wait, the $ g(x) $ graph: the first segment is from (0,1) to (1,5). So yes, $ g(0)=1 $. So $ g(f(2)) = 1 $? Wait, no, that seems wrong. Wait, maybe I misread $ f(2) $. Wait, $ f(x) $ graph: at $ x = 2 $, the point is (2,0), so $ f(2)=0 $. Then $ g(0) $: from $ g(x) $ graph, at $ x = 0 $, the value is 1. So $ g(f(2))=1 $.

Wait, no, maybe I made a mistake in $ g(0) $. Wait, the $ g(x) $ graph: the y - axis is from - 1 to 6. At $ x = 0 $, the point is (0,1). So $ g(0)=1 $. So $ g(f(2)) = 1 $.

# Explanation:
## Step1: Find $ f(2) $
From $ f(x) $ graph, $ f(2)=0 $.
## Step2: Find $ g(0) $
From $ g(x) $ graph, $ g(0)=1 $.
# Answer:
$ g(f(2)) = 1 $

### For $ f(f(3)) $:
# Explanation:
## Step1: Find $ f(3) $
From $ f(x) $ graph, when $ x = 3 $, $ f(3)=3 $.
## Step2: Find $ f(3) $ (again, since $ f(f(3))=f(3) $)
From $ f(x) $ graph, when $ x = 3 $, $ f(3)=3 $. Wait, no, $ f(3)=3 $, so $ f(f(3))=f(3)=3 $? Wait, no, $ f(3)=3 $, so $ f(f(3))=f(3)=3 $? Wait, let's check the $ f(x) $ graph. At $ x = 3 $, the $ f(x) $ graph has a point at (3,3). So $ f(3)=3 $, then $ f(f(3))=f(3)=3 $.
# Explanation:
## Step1: Find $ f(3) $
From $ f(x) $ graph, $ f(3)=3 $.
## Step2: Find $ f(3) $
From $ f(x) $ graph, $ f(3)=3 $.
# Answer:
$ f(f(3)) = 3 $

### For $ g(g(0)) $:
# Explanation:
## Step1: Find $ g(0) $
From $ g(x) $ graph, when $ x = 0 $, $ g(0)=1 $.
## Step2: Find $ g(1) $
From $ g(x) $ graph, when $ x = 1 $, $ g(1)=5 $.
# Explanation:
## Step1: Determine $ g(0) $
From the $ g(x) $ graph, at $ x = 0 $, $ g(0)=1 $.
## Step2: Determine $ g(1) $
From the $ g(x) $ graph, at $ x = 1 $, $ g(1)=5 $.
# Answer:
$ g(g(0)) = 5 $

Final Answers:
$ f(g(4))=\boxed{0} $
$ g(f(2))=\boxed{1} $
$ f(f(3))=\boxed{3} $
$ g(g(0))=\boxed{5} $

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QUESTION IMAGE

Question

Explanation:

For \( f(g(4)) \):

Step1: Find \( g(4) \)

Step2: Find \( f(2) \)

Step1: Find \( f(2) \)

Step2: Find \( g(0) \)

Step1: Find \( f(2) \)

Step2: Find \( g(0) \)

Answer:

For \( g(f(2)) \):