Find a function’s output value when given an input value

Summary

This 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.