Find a function’s output value when given an input value
Summary
TLDRThis script explains the process of finding an input value for a given output in a linear function. It uses the function f(x) = 2x - 2 and demonstrates how to solve for x when f(x) equals -8. The solution involves setting up an equation, isolating the variable, and finding x = -3, which means an input of -3 yields an output of -8. The script also clarifies the distinction between input (x-value) and output (y-value) and how to represent the solution in function notation and as an ordered pair.
Takeaways
- 🔍 The script explains a method to find the input value of a function given a specific output value.
- 📚 The function in question is f(x) = 2x - 2, and the goal is to find the x value that results in an output of -8.
- 🔄 The first step is to set the function equal to the given output value, replacing f(x) with -8.
- 📝 The equation is then rewritten as -8 = 2x - 2, which is a linear equation.
- 🧩 The next step involves solving the linear equation by adding 2 to both sides, resulting in -6 = 2x.
- ➗ To isolate x, both sides of the equation are divided by 2, leading to x = -3.
- 📌 The solution indicates that an input value of -3 for the function will produce an output value of -8.
- 📈 The input and output values are clarified, with x being the input and Y being the output.
- 📑 The script mentions that answers can be given in function notation, where f(x) = y.
- 📝 In function notation, the solution is expressed as f(-3) = -8, which corresponds to an ordered pair.
- 📍 The ordered pair (-3, -8) represents the coordinates where the function intersects with the line y = -8.
- 📘 The script serves as a tutorial on solving for an input value in a linear function given an output value.
Q & A
What is the given function f(x) in the script?
-The given function is f(x) = 2x - 2.
What is the specific output value we are trying to find the input for in the script?
-We are trying to find the input value for the output value of -8.
What is the first step in solving for x when f(x) = -8?
-The first step is to replace f(x) with -8 in the equation, resulting in -8 = 2x - 2.
How do we rewrite the function notation f(x) to represent the output value?
-We replace f(x) with the output value, so it becomes -8 = 2x - 2.
What type of equation are we dealing with in this problem?
-We are dealing with a basic linear equation.
What operation is performed to isolate 2x in the equation -8 = 2x - 2?
-We add 2 to both sides of the equation to isolate 2x, resulting in -6 = 2x.
How do we solve for x after isolating the term 2x?
-We divide both sides of the equation by 2, which gives us x = -3.
What is the input value of x that results in an output of -8 for the function f(x)?
-The input value of x that results in an output of -8 is -3.
How is the input and output values related in function notation?
-In function notation, the input value is represented by x and the output value is represented by y, so f(x) = y.
What is the ordered pair that corresponds to the function f(x) when x = -3?
-The ordered pair is (-3, -8), where -3 is the x-coordinate and -8 is the y-coordinate.
How can the solution be expressed in function notation?
-The solution can be expressed in function notation as f(-3) = -8.
Outlines
🔍 Finding Input for a Given Output in a Linear Function
This paragraph explains the process of finding an input value for a function given a specific output value. The function in question is f(x) = 2x - 2, and the goal is to find the value of x that results in an output of -8. The explanation begins by setting f(x) equal to -8 and then solving the resulting linear equation, -8 = 2x - 2, through basic algebraic steps. The solution involves adding 2 to both sides to isolate the term with x, resulting in -6 = 2x, and then dividing by 2 to find x = -3. The paragraph concludes by emphasizing the relationship between the input value (x) and the output value (y) in function notation, and how to express the solution as an ordered pair (-3, -8) that corresponds to the function.
Mindmap
Keywords
💡Input value
💡Output value
💡Function
💡Linear equation
💡Solving an equation
💡Algebraic manipulation
💡Basic linear equation
💡Function notation
💡Ordered pair
💡X-coordinate and Y-coordinate
Highlights
The process of finding an input value for a given output value in a function is explained.
The function f(x) = 2x - 2 is used as an example to demonstrate the process.
The goal is to find the value of x when f(x) equals -8.
The function notation f(x) is replaced with the output value -8 to set up the equation.
The equation -8 = 2x - 2 is formed by substituting the function with the output value.
Solving the linear equation involves basic algebraic steps.
Adding 2 to both sides of the equation simplifies it to -6 = 2x.
Dividing both sides by 2 yields the solution x = -3.
The input value x = -3 generates the output value f(x) = -8 for the given function.
The relationship between input and output values in a function is clarified.
The importance of understanding the function notation f(x) = y is emphasized.
The solution is presented in function notation as f(-3) = -8.
The concept of ordered pairs in the context of functions is introduced.
The ordered pair (-3, -8) corresponds to the input and output values of the function.
The x-coordinate represents the input value, and the y-coordinate represents the output value.
The process is summarized to ensure understanding of input and output values in functions.
Transcripts
what if we want to find an input value
when we're given a specific output value
let's say we have the function f of X
equals 2x minus 2 and we need to find
the value of x such that f of X equals
negative 8 our first step is to replace
f of X with negative 8 now let's rewrite
our function so f of x equals 2x minus 2
now remember the notation f of X that's
equivalent to Y which is equivalent to
our output value so everywhere I see the
notation f of X I'm going to replace it
with the number negative 8
so that means negative 8 is going to be
on the left side of my equation so now I
have the equation negative 8 equals 2x
minus 2 well hey look at that that's
just a basic linear equation good thing
we already know how to solve that so
that's step 2
so my equation is negative 8 equals 2x
minus 2 so to solve this I would add 2
to both sides
that would give me negative 6 equals 2x
then I would divide both sides by 2 and
I'd get x equals negative 3 so this
tells us that my function f of x equals
negative 8 when the value of x is
negative 3 so that means I need an input
value of negative 3 in order to generate
an output value of negative 8 let's make
sure we have those input and output
values straight my input value is the x
value that's negative 3 that's what I
would need to input in the function in
order to generate an output value of
negative 8
remember the input value is our x value
and the output value is our Y value
sometimes you might be asked to give
your answer in function notation
so remember f of x equals y that's our
general function notation so now if I
want to write f of X I'm going to
replace the X with the input value
negative 3 and then that's going to be
equal to my
output value of negative 8 so for
function notation I would say F of
negative 3 equals negative 8 that
corresponds to an ordered pair that
belongs to this function so since
negative 3 is in the spot of the input
value that is my x-coordinate and since
it equals an output value of negative 8
I use negative 8 as my y-coordinate so
my ordered pair is negative 3 negative 8
Voir Plus de Vidéos Connexes
5.0 / 5 (0 votes)