At Westonci.ca, we provide clear, reliable answers to all your questions. Join our vibrant community and get the solutions you need. Our Q&A platform provides quick and trustworthy answers to your questions from experienced professionals in different areas of expertise. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To find the equation of a linear function that has been shifted down, we need to understand how vertical shifts affect the function.
1. Start with the Parent Function:
The linear parent function is given by [tex]\( f(x) = x \)[/tex]. This is the simplest form of a linear function, representing a straight line passing through the origin with a slope of 1.
2. Understand the Shift:
Shifting a function vertically simply involves adding or subtracting a constant value to the function. Specifically, if we want to shift the function down by a certain number of units, we subtract that number from the function.
3. Apply the Shift:
Here, we are instructed to shift the function down by 6 units. To achieve this, we subtract 6 from the original function [tex]\( f(x) = x \)[/tex].
[tex]\[ g(x) = f(x) - 6 \][/tex]
4. Substitute the Parent Function:
Replace [tex]\( f(x) \)[/tex] with [tex]\( x \)[/tex]:
[tex]\[ g(x) = x - 6 \][/tex]
Thus, the new function after shifting the parent function [tex]\( f(x) = x \)[/tex] down by 6 units is:
[tex]\[ g(x) = x - 6 \][/tex]
5. Identify the Correct Option:
Comparing this to the given options:
- A. [tex]\( g(x) = x + 6 \)[/tex]
- B. [tex]\( g(x) = \frac{1}{6} x \)[/tex]
- C. [tex]\( g(x) = x - 6 \)[/tex]
- D. [tex]\( g(x) = 6x \)[/tex]
The correct option is clearly:
[tex]\[ \boxed{C. \ g(x) = x - 6} \][/tex]
1. Start with the Parent Function:
The linear parent function is given by [tex]\( f(x) = x \)[/tex]. This is the simplest form of a linear function, representing a straight line passing through the origin with a slope of 1.
2. Understand the Shift:
Shifting a function vertically simply involves adding or subtracting a constant value to the function. Specifically, if we want to shift the function down by a certain number of units, we subtract that number from the function.
3. Apply the Shift:
Here, we are instructed to shift the function down by 6 units. To achieve this, we subtract 6 from the original function [tex]\( f(x) = x \)[/tex].
[tex]\[ g(x) = f(x) - 6 \][/tex]
4. Substitute the Parent Function:
Replace [tex]\( f(x) \)[/tex] with [tex]\( x \)[/tex]:
[tex]\[ g(x) = x - 6 \][/tex]
Thus, the new function after shifting the parent function [tex]\( f(x) = x \)[/tex] down by 6 units is:
[tex]\[ g(x) = x - 6 \][/tex]
5. Identify the Correct Option:
Comparing this to the given options:
- A. [tex]\( g(x) = x + 6 \)[/tex]
- B. [tex]\( g(x) = \frac{1}{6} x \)[/tex]
- C. [tex]\( g(x) = x - 6 \)[/tex]
- D. [tex]\( g(x) = 6x \)[/tex]
The correct option is clearly:
[tex]\[ \boxed{C. \ g(x) = x - 6} \][/tex]
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.