name: matthew jelinski 2.07 classwork period: 1st
1. what are the range values of ( f(x)=\frac{1}{2}x + 7 ) with domain values of ({-4, 2, 5})?
(*hint: create a table. )
range { }

path of a golf ball
(graph: height (feet) vs time (seconds))

2. what is the domain?
3. what is the range?
4. is this discrete or continuous
5. is this a function? (why?)
6. what would be the dependent variable? circle answer: height in feet or time(seconds)

for problems 7 thru 10 use the graph below:
(second graph: coordinate plane with plotted points)
7. what is the domain
8. what is the range
9. is this discrete or continuous
10. is this a function? why

Question

name: matthew jelinski  2.07 classwork  period: 1st
1.  what are the range values of ( f(x)=\frac{1}{2}x + 7 ) with domain values of ({-4, 2, 5})?
(*hint: create a table. )
range { }

path of a golf ball
(graph: height (feet) vs time (seconds))

2. what is the domain?
3. what is the range?
4. is this discrete or continuous
5. is this a function? (why?)
6. what would be the dependent variable? circle answer:  height in feet  or  time(seconds)

for problems 7 thru 10 use the graph below:
(second graph: coordinate plane with plotted points)
7. what is the domain
8. what is the range
9. is this discrete or continuous
10. is this a function? why

Accepted Answer

### Problem 1
# Explanation:
## Step1: Substitute $ x = -4 $ into $ f(x)=\frac{1}{2}x + 7 $
$ f(-4)=\frac{1}{2}(-4)+7=-2 + 7 = 5 $
## Step2: Substitute $ x = 2 $ into $ f(x)=\frac{1}{2}x + 7 $
$ f(2)=\frac{1}{2}(2)+7=1 + 7 = 8 $
## Step3: Substitute $ x = 5 $ into $ f(x)=\frac{1}{2}x + 7 $
$ f(5)=\frac{1}{2}(5)+7=\frac{5}{2}+7=\frac{5 + 14}{2}=\frac{19}{2}=9.5 $
# Answer:
$ \{5, 8, 9.5\} $ (or $ \{5, 8, \frac{19}{2}\} $)

### Problem 2 (Path of a Golf Ball - Domain)
# Brief Explanations:
The domain of a graph representing time (x - axis) and height (y - axis) for a golf ball's path is the set of all possible x - values (time) the ball is in motion. From the graph, the time starts at 0 seconds and ends when the ball hits the ground (x = 5 seconds, approximately, from the grid). So the domain is the interval of time the ball is moving, so $ 0\leq x\leq5 $ (or in set notation $ \{x|0\leq x\leq5, x\in\mathbb{R}\} $).
# Answer:
The domain is $ 0\leq x\leq5 $ (or $ [0, 5] $ in interval notation, representing all real numbers from 0 to 5 seconds).

### Problem 3 (Path of a Golf Ball - Range)
# Brief Explanations:
The range is the set of all possible y - values (height). The golf ball starts at height 0, goes up to a maximum height, then comes back down to 0. From the graph, the maximum height is around 100 feet (or as per the grid, the peak y - value). So the range is $ 0\leq y\leq100 $ (or $ [0, 100] $ in interval notation, representing all real numbers from 0 to the maximum height in feet).
# Answer:
The range is $ 0\leq y\leq100 $ (or $ [0, 100] $ in interval notation).

### Problem 4 (Path of a Golf Ball - Discrete or Continuous)
# Brief Explanations:
The path of a golf ball is a continuous curve because time and height can take any real - number value within the interval (you can't have a "jump" in time or height as the ball moves). So it is continuous.
# Answer:
Continuous

### Problem 5 (Path of a Golf Ball - Is it a function?)
# Brief Explanations:
To determine if a graph is a function, we use the vertical line test. For any vertical line (x - value), it intersects the graph at most once. The graph of the golf ball's path is a parabola - like curve, and any vertical line will intersect it at only one point. So it is a function.
# Answer:
Yes, because it passes the vertical line test (each x - value has at most one y - value).

### Problem 6 (Path of a Golf Ball - Dependent Variable)
# Brief Explanations:
The dependent variable depends on the independent variable. Time (seconds) is the independent variable (we can choose a time to measure height), and height (in feet) depends on the time. So the dependent variable is Height in feet.
# Answer:
Height in feet

### Problem 7 (Second Graph - Domain)
# Brief Explanations:
The domain is the set of all x - values of the plotted points. From the table and the graph, the x - values are $ - 2,-1,0,1,2,3 $. So the domain is $ \{-2, - 1,0,1,2,3\} $.
# Answer:
$ \{-2, - 1,0,1,2,3\} $

### Problem 8 (Second Graph - Range)
# Brief Explanations:
The range is the set of all y - values of the plotted points. From the table, the y - values are $ - 3,-2,1,2,3 $. So the range is $ \{-3, - 2,1,2,3\} $.
# Answer:
$ \{-3, - 2,1,2,3\} $

### Problem 9 (Second Graph - Discrete or Continuous)
# Brief Explanations:
The graph consists of discrete points (not a connected curve), so it is discrete.
# Answer:
Discrete

### Problem 10 (Second Graph - Is it a function?)
# Brief Explanations:
To be a function, each x - value must have only one y - value. Looking at the table, the x - value $ - 1 $ has two different y - values ($ - 3 $ and $ 1 $), so it fails the vertical line test (or the definition of a function). Thus, it is not a function.
# Answer:
No, because the x - value $ - 1 $ is paired with more than one y - value (it fails the vertical line test).

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QUESTION IMAGE

Question

Explanation:

Problem 1

Step1: Substitute \( x = -4 \) into \( f(x)=\frac{1}{2}x + 7 \)

Step2: Substitute \( x = 2 \) into \( f(x)=\frac{1}{2}x + 7 \)

Step3: Substitute \( x = 5 \) into \( f(x)=\frac{1}{2}x + 7 \)

Answer:

Problem 2 (Path of a Golf Ball - Domain)