Podcast
Questions and Answers
What is the simplified form of $\sqrt{50x^2}$?
What is the simplified form of $\sqrt{50x^2}$?
- $5x$
- $25\sqrt{2}$
- $10\sqrt{5}x$
- $5\sqrt{2x}$ (correct)
In what real-world scenario would a radical function be used to calculate values?
In what real-world scenario would a radical function be used to calculate values?
- Calculating the area of a square garden
- Calculating the trajectory of a projectile (correct)
- Measuring the volume of a cylindrical tank
- Determining the population growth rate in a city
Which transformation involves graphing a radical function by compressing or expanding it?
Which transformation involves graphing a radical function by compressing or expanding it?
- Rotation
- Reflection
- Translation
- Dilation (correct)
For the function $f(x) = \sqrt{6x - 3}$, what is the domain of the function?
For the function $f(x) = \sqrt{6x - 3}$, what is the domain of the function?
Which of the following can be a solution to the equation $\sqrt{x + 5} = -3$?
Which of the following can be a solution to the equation $\sqrt{x + 5} = -3$?
What is an example of a real-world application where radical functions are commonly used?
What is an example of a real-world application where radical functions are commonly used?
Study Notes
Radical Functions
Simplifying Radical Expressions
Simplifying radical expressions involves isolating the radical and raising both sides of the equation to the power of the index. No perfect squares are allowed in the radicand, no fractions in the radicand, and no radicals in the denominator of a fraction.
Example: Simplify √(25x^2)
Solution: 5x
Real-World Applications of Radical Functions
Radical functions are used in various real-world applications, such as in physics for calculating the distance of an object, in finance for calculating interest, and in economics for calculating growth.
Example: A ball is thrown vertically upward from the ground with an initial velocity of 60 m/s. Its height above the ground after t seconds is given by h(t) = 60√(1 - (t/9.8)).
Applying Radical Function Transformations
Transformations of radical functions include reflections, translations, and compressions/expansions.
Example: Graph the function √(x - 2) by reflecting the graph of √x about the vertical axis.
Graphing Radical Functions
Graphing radical functions involves plotting points and identifying the domain and range.
Example: Graph the function g(x) = √(5x + 1) by choosing points that give easy radicands.
Solving Radical Equations
Solving radical equations involves isolating the radical and raising both sides of the equation to the power of the index.
Example: Solve the equation √(x - 1) = 2.
Solution: x = 5
Thoughtful Word-Problems Relating to Radical Functions
Thoughtful word-problems can be created by relating radical functions to real-world situations, such as calculating the time it takes for a ball to return to the ground after being thrown vertically upward.
Example: A ball is thrown vertically upward from a height of 50 meters with an initial velocity of 30 m/s. How long does it take for the ball to return to the ground?
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Description
Test your knowledge on simplifying radical expressions, real-world applications, function transformations, graphing, solving equations, and thoughtful word-problems related to radical functions.
