Scaling functions introduction | Transformations of functions | Algebra 2 | Khan Academy | Summary and Q&A

TL;DR

Learn how to scale functions using Desmos, an online graphing calculator, by multiplying the function by a constant or replacing the x variable with a constant times x.

Key Insights

• 🔨 Desmos is a useful tool for understanding function scaling.
• ✖️ Scaling a function involves multiplying the function by a constant or replacing the x variable with a constant times x.
• 😀 Increasing the constant in the scaling equation increases the slope and y-intercept, while decreasing the constant decreases them.
• 🅰️ Scaling can be applied to various types of functions, including quadratic, linear, exponential, and trigonometric functions.
• 🏛️ Experimenting with different constants and functions in Desmos can help build an intuitive understanding of function scaling.
• ☠️ Increasing the constant in the scaling equation for a quadratic function changes the rate at which the parabola increases or decreases.
• 💱 Scaling a function can also change its y-intercept, depending on the constant used.

Transcript

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Questions & Answers

Q: How can Desmos be used to understand function scaling?

Desmos is an online graphing calculator that allows users to input functions and see the effects of scaling. By multiplying the function by a constant or replacing the x variable with a constant times x, you can observe how the slope and y-intercept change.

Q: What happens when the constant in the scaling equation is increased or decreased?

Increasing the constant in the scaling equation for an absolute value function increases both the slope and the y-intercept. Decreasing the constant has the opposite effect, decreasing both the slope and the y-intercept.

Q: How does scaling a quadratic function differ from scaling an absolute value function?

Scaling a quadratic function involves similar principles to scaling an absolute value function. Increasing the constant in the scaling equation for a quadratic function changes the rate at which the parabola increases or decreases. Decreasing the constant has the opposite effect.

Q: What other types of functions can be scaled using Desmos?

Desmos can be used to scale various types of functions, including linear, exponential, and trigonometric functions. By experimenting with different functions, users can observe how scaling affects their shape, slope, and y-intercept.

Summary & Key Takeaways

• Desmos is an online graphing calculator that can be used to understand function scaling.

• Scaling a function involves multiplying the function by a constant or replacing the x variable with a constant times x.

• When scaling an absolute value function, increasing the constant increases the slope and y-intercept, while decreasing the constant decreases them.