The graph of y against x2 is shown. The rule connecting x and y is:

Question

BlackTom AI · Accepted Answer

First, observe that the graph plots y against x^2, with the origin at (0,0) and a straight line passing through it, indicating a direct proportionality between y and x^2.
Option a: y = 3x. This would imply a linear relationship between y and x, not between y and x^2, and would produce a line with slope relative to x, which does not fit a plot of y versus x^2.
Option b: y = 1.5x2. Here, x2 denotes x squared; the expression represents y being proportional to x^2 with a coefficient of 1.5. This matches a straight line through the origin when the horizontal axis is x^2, because y = (1.5) · (x^2) is linear in x^2.
Option c: y = 3x2. This also expresses y proportional to x^2, but with a steeper slope (3) than what the graph shows. Since the line in the graph appears less steep, this overestimates the proportionality constant.
Option d: y = 1.5x. This would imply a linear relationship between y and x, not between y and x^2, and would produce a line with respect to x, not x^2, contradicting the given axis correspondence.
In summary, the key clues are the axes being y versus x^2 and the line passing through the origin with a specific slope. The expression that matches a proportional relationship y ∝ x^2 with a coefficient around 1.5 aligns with the graph’s slope, whereas the other options misalign either the variable (x vs x^2) or the steepness, or both.

MUF0141 Fund. Mathematics Unit 1 - Semester 2, 2025 3.3 Non-linear Relations Quiz (Formative)

The graph of y against x2 is shown. The rule connecting x and y is:

View Explanation

Log in for full answers

Similar Questions

Quadratic Function For the function defined by , find the following values. Simply your answers. [Fill in the blank] [Fill in the blank] [Fill in the blank] [Fill in the blank]

Let be a quadratic function. Suppose we have given the following information: and . Which of the following answers are correct (Please note that exactly two are correct). If you cannot find the formula of the function, you still can find the shape of its graph by using a graphical argument.

An equation of the graph shown could be:

The graph of [math: y] versus [math: x2] x^2 is shown. The rule connecting [math: y] and [math: x] is :

MTH1010_05_10_4

MTH1010_05_04_1

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler