identifying key characteristics of graphs of functions
use the graph to answer all of the questions.
select the number of y - intercepts
select the number of x - intercepts
does the function have a minimum x - value? ● yes ● no
does the function have a maximum x - value? ● yes ● no
select a statement to describe the domain
does the function have a minimum y - value? ● yes ● no
does the function have a maximum y - value? ● yes ● no
select a statement to describe the range

Question

Accepted Answer

### 1. Number of y - intercepts
# Explanation:
## Step1: Recall y - intercept definition
A y - intercept is a point where the graph intersects the y - axis (where $x = 0$). Looking at the graph, we check if there is a point with $x=0$. From the graph, we can see that there is 1 point where the graph intersects the y - axis.
# Answer: 1

### 2. Number of x - intercepts
# Explanation:
## Step1: Recall x - intercept definition
An x - intercept is a point where the graph intersects the x - axis (where $y = 0$). Looking at the graph, we check if there is a point with $y = 0$. From the graph, we can see that there is 1 point where the graph intersects the x - axis.
# Answer: 1

### 3. Does the function have a minimum x - value?
# Explanation:
## Step1: Analyze the domain (x - values)
Looking at the graph, the x - values seem to start from a certain point (the left - most point) and go towards $x = 0$ (and maybe beyond, but from the visible part, the left - most x - value is a specific number, but since the graph has a left - most point, the x - values have a minimum (the smallest x - value on the graph). Wait, no, looking at the x - axis labels, the left - most x - value is around $x=- 14$ or so? Wait, no, the graph on the left: the x - axis has negative values on the left. Wait, actually, the graph of the curve: the x - values of the curve start from a left - most point (the left - most x - coordinate) and go towards $x = 0$. But the other part (the horizontal line) is at $y = 0$ from $x = 0$ to the right? Wait, no, the horizontal line is at $y = 0$ starting from $x = 0$ and going to the right? Wait, no, the graph: the upper curve is from the left (negative x - values) towards $x = 0$, and the lower horizontal line is from $x = 0$ to the right (positive x - values) at $y = 0$. Wait, for the function (the combination of the curve and the line), the x - values of the curve start from a left - most x - value (the smallest x - value on the curve). But does the function have a minimum x - value? The curve has a left - most point, so the x - values of the curve have a minimum. But the horizontal line starts at $x = 0$ and goes to the right. But the function is the combination? Wait, maybe the function is the union of the curve and the horizontal line? Wait, no, maybe it's a piece - wise function. But from the graph, the curve is on the left (negative x - values) and the horizontal line is on the right (non - negative x - values). The curve has a left - most x - value (the smallest x - value for the curve), so the function (the entire graph) has a minimum x - value (the left - most x - value of the curve). Wait, but maybe I made a mistake. Wait, the x - axis: the left - most x - value on the graph (the curve) is a specific number, so the x - values of the function have a minimum (the smallest x - value). So the answer is Yes? Wait, no, wait the curve: the x - values of the curve are from, say, $x=-14$ (or whatever the left - most x is) up to $x = 0$, and the horizontal line is from $x = 0$ to $x=\infty$ (or as far as the graph shows). So the x - values of the function (the entire graph) have a minimum x - value (the left - most x of the curve). So the answer is Yes.
# Answer: Yes

### 4. Does the function have a maximum x - value?
# Explanation:
## Step1: Analyze the domain (x - values)
The x - values of the function (the horizontal line) go to the right (positive x - values) without a visible end (the graph extends to the right). So there is no maximum x - value (since x can get as large as possible). So the answer is No.
# Answer: No

### 5. Does the function have a minimum y - value?
# Explanation:
## Step1: Analyze the range (y - values)
Looking at the graph, the y - values of the function: the horizontal line is at $y = 0$, and the curve is above $y = 0$ (since the curve's y - values are greater than 0). So the smallest y - value is $y = 0$ (from the horizontal line). So the function has a minimum y - value (0). So the answer is Yes.
# Answer: Yes

### 6. Does the function have a maximum y - value?
# Explanation:
## Step1: Analyze the range (y - values)
Looking at the curve, the y - value at the left - most point of the curve is the highest y - value (since the curve is decreasing as x increases towards 0). So there is a maximum y - value (the y - value of the left - most point of the curve). So the answer is Yes.
# Answer: Yes

### 7. Domain description (assuming options like "all real numbers", "x ≤ a", "x ≥ a" etc.)
# Explanation:
## Step1: Analyze x - values
From the graph, the curve is on the left (negative x - values up to $x = 0$) and the horizontal line is on the right (from $x = 0$ to positive infinity). So the domain (x - values) includes all real numbers from the left - most x (which is a specific number, but if we consider the entire function, it seems like the x - values start from a left - most point (maybe $x=-\infty$? No, the curve has a left - most point. Wait, no, looking at the x - axis labels, the left - most x is around $x=-14$, but maybe the function's domain is all real numbers? Wait, no, the curve is from a left - most x (say $x = - 14$) to $x = 0$, and the horizontal line is from $x = 0$ to $x=\infty$. So the domain is all real numbers (since the curve covers from the left - most x to 0, and the line covers from 0 to $\infty$, so together, all real numbers). Or maybe the domain is $x\geq$ (the left - most x). But if we assume the curve is defined for all x from $-\infty$ to 0 (but the graph shows a left - most point), maybe the domain is all real numbers. But more likely, the domain is $x$ such that $x$ is from the left - most x (the minimum x) to $\infty$, but since the horizontal line starts at $x = 0$ and goes to the right, and the curve is from the left to 0, the domain is all real numbers (because the curve's left - most x is a finite number, but maybe the function is defined for all x. Alternatively, if the curve is from $x=-\infty$ to 0 and the line is from 0 to $\infty$, then the domain is all real numbers. So the domain is all real numbers (or $x\in(-\infty,\infty)$).
# Answer: All real numbers (or the appropriate option from the dropdown, e.g., "All real numbers" if that's an option)

### 8. Range description (assuming options like "all real numbers", "y ≤ a", "y ≥ a" etc.)
# Explanation:
## Step1: Analyze y - values
The minimum y - value is 0 (from the horizontal line) and the maximum y - value is the y - value of the left - most point of the curve (say $y = 10$ or so from the graph). So the range is $0\leq y\leq$ (maximum y - value). So the range is $y$ such that $0\leq y\leq$ (the maximum y - value). If the options are like "y ≥ 0" or "0 ≤ y ≤ a", then it's $0\leq y\leq$ (maximum y).
# Answer: $0\leq y\leq$ (the maximum y - value from the graph, e.g., if the maximum y is 10, then $0\leq y\leq10$)

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QUESTION IMAGE

Question

Explanation:

1. Number of y - intercepts

Step1: Recall y - intercept definition

Step1: Recall x - intercept definition

Step1: Analyze the domain (x - values)

Answer:

2. Number of x - intercepts