- #1
nick850
- 14
- 0
Homework Statement
if f(x) = 10-x²
f(x + h) = ?
Homework Equations
not applicable
The Attempt at a Solution
no clue
What is f(x + h) if f(x) = 10-x²?
- Thread starter nick850
- Start date
In summary, the function f(x) = 10-x² is a quadratic function that can be used to model real-world situations and solve mathematical problems. The function f(x + h) is a shifted version of f(x) = 10-x² with a horizontal shift of h units. To find the value of f(x + h), you can substitute x + h into the function. Changing the value of h affects the graph of f(x + h) by shifting it horizontally. f(x + h) can be equal to f(x) when h = 0, resulting in no horizontal shift.
if f(x) = 10-x²
f(x + h) = ?
not applicable
no clue
- #2
jegues
- 1,097
- 3
Simply plug,
[tex](x+h)[/tex]
Into all the terms that contain an [tex]x[/tex].
[tex](x+h)[/tex]
Into all the terms that contain an [tex]x[/tex].
- #3
nick850
- 14
- 0
thank you!
- #4
Mentallic
Homework Helper
- 3,802
- 95
Yep it's as simple as that!
[tex]f(x)=10-x^2[/tex]
[tex]f(x+h)=10-(x+h)^2[/tex]
[tex]f(a)=10-a^2[/tex]
[tex]f(2)=10-2^2=6[/tex]
[tex]f(\sqrt{10})=10-(\sqrt{10})^2=0[/tex]
I think you get the point
Oh and if you choose some number a such that f(a)=0, this means that a is a root of the equation y=f(x). Such as that last example with the [itex]\sqrt{10}[/itex].
[tex]f(x)=10-x^2[/tex]
[tex]f(x+h)=10-(x+h)^2[/tex]
[tex]f(a)=10-a^2[/tex]
[tex]f(2)=10-2^2=6[/tex]
[tex]f(\sqrt{10})=10-(\sqrt{10})^2=0[/tex]
I think you get the point
Oh and if you choose some number a such that f(a)=0, this means that a is a root of the equation y=f(x). Such as that last example with the [itex]\sqrt{10}[/itex].
FAQ: What is f(x + h) if f(x) = 10-x²?
What is the purpose of the function f(x) = 10-x²?
The function f(x) = 10-x² is a quadratic function that can be used to model various real-world situations, such as the height of an object thrown into the air or the profit of a business over time. It can also be used to solve mathematical problems involving quadratic equations.
How is the function f(x + h) related to f(x) = 10-x²?
The function f(x + h) is a shifted version of f(x) = 10-x². It represents the same quadratic function, but with a horizontal shift of h units to the left or right depending on the value of h. This shift does not change the overall shape or characteristics of the function.
3. How do you find the value of f(x + h) using the function f(x) = 10-x²?
To find the value of f(x + h), you can simply substitute the value of x + h into the function f(x) = 10-x². For example, if the function is f(x) = 10-x² and you want to find f(3), you can substitute 3 for x in the function to get f(3) = 10-(3)² = 1. This means that when x = 3, the value of the function is 1.
4. How does changing the value of h affect the graph of f(x + h)?
Changing the value of h will shift the graph of f(x + h) horizontally. If h is positive, the graph will shift to the left, and if h is negative, the graph will shift to the right. The amount of the shift is equal to the absolute value of h. For example, if h = 2, the graph will shift 2 units to the left, and if h = -4, the graph will shift 4 units to the right.
5. Can f(x + h) ever be equal to f(x)?
Yes, f(x + h) can be equal to f(x) if h = 0. In this case, the graph of f(x + h) will overlap with the graph of f(x) and there will be no horizontal shift. This means that the value of the function remains the same regardless of the value of x, making f(x + h) equal to f(x) for all values of x.