The graph of a function fis shown below. Find f (1) and find one value of X for whichf (x) = - 1. ) s(1) = O (b) One value of z for which (:) = -1 : 0

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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The graph of a function f is shown below.
Findf(1) and find one value of x for which f(x)=-1.

### Analyzing the Graph of a Function

The graph of a function \( f \) is shown below. This graph can be used to determine the value of \( f(1) \) and find one value of \( x \) for which \( f(x) = -1 \). 

To analyze the graph:

1. **Identify \( f(1) \):**
   - To find \( f(1) \), locate the point on the graph where \( x = 1 \) and determine the corresponding \( y \)-value (the \( y \)-coordinate of this point).

2. **Finding \( x \) where \( f(x) = -1 \):**
   - Look for the locations on the graph where the function value (the \( y \)-value) is -1. Determine the corresponding \( x \)-values for these points.

#### Graph Description
The provided graph is a parabola that opens upwards. It is symmetric about the y-axis. It intersects the y-axis at approximately -4 and the x-axis at -2 and 2.

#### Problem and Solution
(a) \( f(1) = \) [To be determined from the graph; look for the y-coordinate where x = 1]
(b) One value of \( x \) for which \( f(x) = -1 \) is \( x = \) [To be determined from the graph; observe where the y-coordinate is -1]

### Detailed Steps

To solve part (a):
- Locate \( x = 1 \) on the x-axis.
- Find the y-coordinate of the point where the vertical line \( x = 1 \) intersects the parabola.
- The intersection occurs at the point (1, -3). Therefore, \( f(1) = -3 \).

To solve part (b):
- Identify where the y-coordinate is -1 on the graph.
- These points appear to be where the parabola intersects the horizontal line \( y = -1 \).
- Observing the horizontal line \( y = -1 \), it intersects the graph at two points. These points are \( x = -1.5 \) and \( x = 1.5 \).

Thus, the solutions are:
(a) \( f(1) = -3 \)

(b) One value of \( x \) for which \( f(x) = -1 \) is \( x = 1.
Transcribed Image Text:### Analyzing the Graph of a Function The graph of a function \( f \) is shown below. This graph can be used to determine the value of \( f(1) \) and find one value of \( x \) for which \( f(x) = -1 \). To analyze the graph: 1. **Identify \( f(1) \):** - To find \( f(1) \), locate the point on the graph where \( x = 1 \) and determine the corresponding \( y \)-value (the \( y \)-coordinate of this point). 2. **Finding \( x \) where \( f(x) = -1 \):** - Look for the locations on the graph where the function value (the \( y \)-value) is -1. Determine the corresponding \( x \)-values for these points. #### Graph Description The provided graph is a parabola that opens upwards. It is symmetric about the y-axis. It intersects the y-axis at approximately -4 and the x-axis at -2 and 2. #### Problem and Solution (a) \( f(1) = \) [To be determined from the graph; look for the y-coordinate where x = 1] (b) One value of \( x \) for which \( f(x) = -1 \) is \( x = \) [To be determined from the graph; observe where the y-coordinate is -1] ### Detailed Steps To solve part (a): - Locate \( x = 1 \) on the x-axis. - Find the y-coordinate of the point where the vertical line \( x = 1 \) intersects the parabola. - The intersection occurs at the point (1, -3). Therefore, \( f(1) = -3 \). To solve part (b): - Identify where the y-coordinate is -1 on the graph. - These points appear to be where the parabola intersects the horizontal line \( y = -1 \). - Observing the horizontal line \( y = -1 \), it intersects the graph at two points. These points are \( x = -1.5 \) and \( x = 1.5 \). Thus, the solutions are: (a) \( f(1) = -3 \) (b) One value of \( x \) for which \( f(x) = -1 \) is \( x = 1.
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