Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Let's analyze the linear function \( f(x) = 2x - 8 \) step-by-step:
### (a) x-intercept
To find the x-intercept, we need to set \( f(x) = 0 \) and solve for \( x \).
[tex]\[ 0 = 2x - 8 \][/tex]
Solving for \( x \):
[tex]\[ 2x = 8 \implies x = 4 \][/tex]
Thus, the x-intercept is \( (4, 0) \).
### (b) y-intercept
To find the y-intercept, we need to set \( x = 0 \) and solve for \( f(x) \).
[tex]\[ y = 2(0) - 8 \][/tex]
Simplifying this:
[tex]\[ y = -8 \][/tex]
Thus, the y-intercept is \( (0, -8) \).
### (c) Domain
The domain of any linear function is all real numbers. This is because a line extends infinitely in both directions along the x-axis.
So, the domain is \( \text{all real numbers} \).
### (d) Range
Similarly, the range of any linear function is all real numbers. This is because a line extends infinitely in both directions along the y-axis.
So, the range is \( \text{all real numbers} \).
### (e) Slope of the line
The slope of the linear function \( f(x) = 2x - 8 \) is the coefficient of \( x \). Here, the slope is \( 2 \).
### Graphing the function
To graph the function \( f(x) = 2x - 8 \), we use the intercepts as reference points. Plot the x-intercept \( (4, 0) \) and the y-intercept \( (0, -8) \) on a coordinate plane. Draw a straight line through these points to represent the linear function.
In summary:
- The x-intercept is \((4, 0)\),
- The y-intercept is \((0, -8)\),
- The domain is all real numbers,
- The range is all real numbers,
- The slope is \(2\).
You can now use these points and information to graph the linear function accurately.
### (a) x-intercept
To find the x-intercept, we need to set \( f(x) = 0 \) and solve for \( x \).
[tex]\[ 0 = 2x - 8 \][/tex]
Solving for \( x \):
[tex]\[ 2x = 8 \implies x = 4 \][/tex]
Thus, the x-intercept is \( (4, 0) \).
### (b) y-intercept
To find the y-intercept, we need to set \( x = 0 \) and solve for \( f(x) \).
[tex]\[ y = 2(0) - 8 \][/tex]
Simplifying this:
[tex]\[ y = -8 \][/tex]
Thus, the y-intercept is \( (0, -8) \).
### (c) Domain
The domain of any linear function is all real numbers. This is because a line extends infinitely in both directions along the x-axis.
So, the domain is \( \text{all real numbers} \).
### (d) Range
Similarly, the range of any linear function is all real numbers. This is because a line extends infinitely in both directions along the y-axis.
So, the range is \( \text{all real numbers} \).
### (e) Slope of the line
The slope of the linear function \( f(x) = 2x - 8 \) is the coefficient of \( x \). Here, the slope is \( 2 \).
### Graphing the function
To graph the function \( f(x) = 2x - 8 \), we use the intercepts as reference points. Plot the x-intercept \( (4, 0) \) and the y-intercept \( (0, -8) \) on a coordinate plane. Draw a straight line through these points to represent the linear function.
In summary:
- The x-intercept is \((4, 0)\),
- The y-intercept is \((0, -8)\),
- The domain is all real numbers,
- The range is all real numbers,
- The slope is \(2\).
You can now use these points and information to graph the linear function accurately.
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.