Skip to main content
Ch. 3 - Polynomial and Rational Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 3 - Polynomial and Rational FunctionsProblem 54
Chapter 4, Problem 54

What happens to y if y varies directly as x, and x is halved?

Verified step by step guidance
1
Understand the concept of direct variation: If y varies directly as x, it means that y is equal to a constant k multiplied by x. This can be written as the equation \(y = k \times x\), where k is a constant.
Identify what happens when x is halved: If the original value of x is changed to \(\frac{x}{2}\), substitute this new value into the direct variation equation.
Write the new equation for y when x is halved: \(y_{new} = k \times \frac{x}{2}\).
Simplify the expression: \(y_{new} = \frac{kx}{2}\).
Compare the new y value to the original y value: Since the original y was \(y = kx\), the new y is exactly half of the original y, meaning y is halved when x is halved.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Direct Variation

Direct variation describes a relationship where one variable is a constant multiple of another, expressed as y = kx. If x changes, y changes proportionally, maintaining the constant ratio k.
Recommended video:
02:44
Maximum Turning Points of a Polynomial Function

Effect of Scaling the Independent Variable

When the independent variable x is scaled by a factor, the dependent variable y changes by the same factor in direct variation. For example, halving x results in y being halved as well.
Recommended video:
5:54
Probability of Multiple Independent Events

Constant of Proportionality

The constant k in y = kx remains unchanged when x changes. It defines the fixed ratio between y and x, ensuring that y varies directly and proportionally with x.
Recommended video:
6:02
Stretches & Shrinks of Functions
Related Practice
Textbook Question

Connecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.)

1748
views
Textbook Question

Solve each rational inequality. Give the solution set in interval notation. (x - 1)/(x - 4) > 0

579
views
Textbook Question

Find a polynomial function ƒ(x) of degree 3 with real coefficients that satisfies the given conditions. Zeros of -2, 1, and 0; ƒ(-1)=-1

458
views
Textbook Question

For each polynomial function, identify its graph from choices A–F.

ƒ(x)=−(x−2)2(x−5) ƒ(x)=-(x-2)^2(x-5)

1107
views
Textbook Question

For each polynomial function, identify its graph from choices A–F. ƒ(x)=(x-2)2(x-5)

843
views
Textbook Question

Solve each rational inequality. Give the solution set in interval notation. (x + 1)/(x - 5) > 0

542
views