1. does the table represent a linear function? explain.
2. does y = x² + 1 represent a linear or non - linear function? explain.
3. the linear function m = 200 - 50v represents the amount m (in dollars) of money that you have after buying v video games.
a. interpret the terms and coefficient in the equation. what do they mean?
b. find the domain of the function. is it discrete or continuous? explain.
c. make a table and a graph using the domain.

Question

1. does the table represent a linear function? explain.
2. does y = x² + 1 represent a linear or non - linear function? explain.
3. the linear function m = 200 - 50v represents the amount m (in dollars) of money that you have after buying v video games.
 a. interpret the terms and coefficient in the equation. what do they mean?
 b. find the domain of the function. is it discrete or continuous? explain.
 c. make a table and a graph using the domain.

Accepted Answer

### 2.
# Brief Explanations:
A linear function has the form $y = mx + b$ where the highest power of $x$ is $1$. In the function $y=x^{2}+1$, the power of $x$ is $2$. Since the exponent of $x$ is not $1$, it does not fit the form of a linear function.
# Answer:
Non - linear function. Because the highest power of $x$ is $2$ (not $1$ as in $y = mx + b$ for linear functions).

### 3a.
# Brief Explanations:
- **$m$**: It is the dependent variable. In the context of the problem, it represents the amount of money (in dollars) remaining after buying video games.
- **$v$**: It is the independent variable. Here, $v$ represents the number of video games bought.
- **Coefficient $- 50$**: It represents the rate at which the money ($m$) changes with respect to the number of video games ($v$). For each video game bought ($v$ increases by $1$), the amount of money $m$ decreases by $50$ dollars.
- **Constant term $200$**: It is the initial value of $m$ when $v = 0$ (i.e., the amount of money you start with before buying any video games).
# Answer:
- $m$: Amount of money (in dollars) remaining.
- $v$: Number of video games bought.
- Coefficient $-50$: Money decreases by $50$ dollars per video game.
- Constant $200$: Initial amount of money.

### 3b.
# Brief Explanations:
We know that $m\geq0$ (since it represents money). So we set up the inequality $200-50v\geq0$. Solving for $v$:
$$
\begin{align*}
200-50v&\geq0\
- 50v&\geq - 200\
v&\leq4
\end{align*}
$$
Also, $v\geq0$ (can't buy a negative number of video games). So the domain is $0\leq v\leq4$. Since $v$ represents the number of video games (which can only be whole numbers like $0,1,2,3,4$), the domain is discrete.
# Answer:
Domain: $0\leq v\leq4$ (where $v$ is an integer). Discrete. Because the number of video games ($v$) must be a whole number (can't buy a fraction of a video game).

### 3c.
# Brief Explanations:
| $v$ | $m = 200-50v$ |
|---|---|
| $0$ | $m=200 - 50\times0=200$ |
| $1$ | $m=200-50\times1 = 150$ |
| $2$ | $m=200-50\times2=100$ |
| $3$ | $m=200-50\times3 = 50$ |
| $4$ | $m=200-50\times4=0$ |

To graph:
- Plot the points $(0,200)$, $(1,150)$, $(2,100)$, $(3,50)$, $(4,0)$ on a coordinate plane.
- Since the domain is discrete (points only at $v = 0,1,2,3,4$), we just connect the points with line - segments (but note that the function is only defined at those discrete $v$ values).
# Answer:
Table:
| $v$ | $m$ |
|----|----|
| $0$ | $200$ |
| $1$ | $150$ |
| $2$ | $100$ |
| $3$ | $50$ |
| $4$ | $0$ |

Graph: Plot discrete points $(0,200)$, $(1,150)$, $(2,100)$, $(3,50)$, $(4,0)$ and connect them with line - segments (function is defined only at $v = 0,1,2,3,4$).

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QUESTION IMAGE

Question

Explanation:

2.

Answer:

3a.