Question

Use the graph to determine the following.  
a. the​ function's domain
b. the​ function's range
c. the​ x-intercepts, if any
d. the​ y-intercept, if any
e. the function values f left parenthesis 0 right parenthesis and f left parenthesis 2 right parenthesis
Assume that the graph of the function continues its trend beyond the displayed coordinate grid.
-10
-5
5
10
-10
-5
5
10
x
y



A coordinate system has a horizontal x-axis labeled from negative 10 to 10 in increments of 1 and a vertical y-axis labeled from negative 10 to 10 in increments of 1. A V-shaped graph that opens downward has vertex (1, negative 4) and passes through the points (0, negative 5), (2, negative 5), and (3, negative 6).
Question content area bottom
Part 1
a. What is the​ function's domain?
  
enter your response here ​(Type your answer in interval​ notation.)
Part 2
b. What is the​ function's range?
  
enter your response here ​(Type your answer in interval​ notation.)
Part 3
c. Find the​ x-intercept(s), if there are any. Select the correct choice below and fill in any answer boxes within your choice.
A.
The​ x-intercept(s) is(are)
  
enter your response here.
​(Type an integer. Use a comma to separate answers as​ needed.)
B.
There is no​ x-intercept.
Part 4
d. Find the​ y-intercept, if there is one. Select the correct choice below and fill in any answer boxes within your choice.
A.
The​ y-intercept is
  
enter your response here.
​(Type an​ integer.)
B.
There is no​ y-intercept.
Part 5
e. Find the values of the function.
f left parenthesis 0 right parenthesisequals
  
enter your response here
f left parenthesis 2 right parenthesisequals
  
enter your response here
What is the function's domain?(Type your answer in interval notation.)What is the function's range?(Type your answer in interval notation.))Select the correct choice below and fill in any answer boxes within your choice.input field 4Select the correct choice below and fill in any answer boxes within your choice.f left parenthesis 0 right parenthesisf left parenthesis 2 right parenthesisf left parenthesis 2 right parenthesis

Answer 1

Let's examine the problem based on the provided description of the graph, which is a V-shaped function that opens downward with a vertex at (1, -4) and passes through the given points.

### Part 1: The function's domain
The domain of a function is the set of all possible input values (x-values). Since the graph continues indefinitely in both directions (to the left and right), the domain is all real numbers.

**Answer:** \((-∞, ∞)\)

### Part 2: The function's range
The range of a function is the set of all possible output values (y-values). Since the V-shaped graph opens downward and has a maximum point at the vertex (1, -4), the highest point on the graph is -4. The graph continues downwards to negative infinity.

**Answer:** \((-∞, -4]\)

### Part 3: The x-intercepts
The x-intercepts are the points where the graph crosses the x-axis (where \(y = 0\)). To find the x-intercepts, we can see from the description that the graph has a vertex at (1,-4) and goes through the points (0, -5) and (2, -5). To find where it crosses the x-axis, we can plot or examine the value of y as a function of x and find when y = 0.

To solve for the x-intercepts mathematically, we can assume the form of the quadratic based on the vertex and find when it equals zero. However, you have described the values, and we can conclude it has a downward opening and negative values only, meaning:

**Answer:** A. The x-intercept(s) is (are) **not present.** (If required to list it, it would often be set as "None" or "does not exist.")

### Part 4: The y-intercept
The y-intercept is where the graph crosses the y-axis (where \(x = 0\)). From the point (0, -5) given, we see the graph crosses at this point.

**Answer:** A. The y-intercept is **-5.**

### Part 5: The function values
To find \(f(0)\) and \(f(2)\):
- \(f(0)\): From the point (0, -5), we directly see that \(f(0) = -5\).
- \(f(2)\): From the point (2, -5), we see that \(f(2) = -5\).

**Answer:**
- \(f(0) = -5\)
- \(f(2) = -5\)

Putting these all together:

- **Domain**: \((-∞, ∞)\)
- **Range**: \((-∞, -4]\)
- **x-intercepts**: None
- **y-intercept**: -5
- **Function values**: \(f(0) = -5\), \(f(2) = -5\)