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

Question

BlackTom AI · Accepted Answer

The problem asks to determine the rule connecting y and x^2 from the given graph of y versus x^2.
First, observe the plotted point on the graph: (x^2, y) = (2, 40). This means when x^2 equals 2, y equals 40.
If y is a function of x^2, the relationship can be written in the form y = m*(x^2), where m is the slope of the line in the y versus x^2 plot.
To find m, compute m = y / (x^2) = 40 / 2 = 20. Therefore, the equation is y = 20*(x^2).
Now evaluate each option:
- Option A: y = 20x^2. This matches the derived relation y = 20*(x^2), so it is consistent with the graph data.
- Option B: y = 20x. This expresses a linear relationship in x rather than in x^2, which does not fit a plot of y versus x^2 and would not pass through the given point when x^2 = 2.
- Option C: y = 40x^2. This would require y to be 40 when x^2 = 1, contradicting the observed value y = 40 when x^2 = 2, so it overestimates the slope.
- Option D: y = 0.1x^2. This implies a much smaller slope (0.1) than what the graph indicates, making it incompatible with the point (2, 40).
Thus, the option that correctly describes the rule connecting y and x^2 is the one that yields y = 20*(x^2) based on the provided point on the graph.

MUF0141 Fund. Mathematics Unit 1 - Semester 2, 2025

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

MTH1010_05_10_4

MTH1010_05_04_1

Apply your understanding of quadratic functions and transformations, and sketch: 𝑦 = 0.25 ( 𝑥 + 6 ) 2 − 4 In this quiz, type the y-intercept in the box. AND Sketch on paper. Label the vertex and the intercepts, with their coordinates. (Answer in quiz: 1 mark) (Written answer: 2 marks)

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