Understanding Functions and Relations

Understanding Functions and Relations

Assessment

Interactive Video

Mathematics

8th - 12th Grade

Medium

Created by

Mia Campbell

Used 1+ times

FREE Resource

The video explores the mathematical relation x = y^2 + 3, questioning if y can be expressed as a function of x. Initially, x is shown as a function of y. The video then attempts to solve for y, revealing that y can be either the positive or negative square root of (x-3). This leads to a graphical representation showing two possible y-values for each x, indicating that y cannot be a function of x, as a function must map each input to a single output.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial relation given in the video?

x = y^2 + 3

y = x^2 + 3

x = y^2 - 3

y = x^2 - 3

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is x represented in terms of y in the initial relation?

As a variable

As a function of x

As a function of y

As a constant

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in solving for y in terms of x?

Add 3 to both sides

Subtract 3 from both sides

Multiply both sides by 3

Divide both sides by 3

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the possible solutions for y when solving x = y^2 + 3?

Both positive and negative square roots of x - 3

Neither positive nor negative square roots of x - 3

Only the negative square root of x - 3

Only the positive square root of x - 3

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why can't y be represented as a function of x in this relation?

Because x maps to multiple y values

Because y maps to multiple x values

Because y has no real solutions

Because x and y are independent

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the graph of y = positive square root of (x - 3) look like?

A parabola opening upwards

A half-parabola opening to the left

A half-parabola opening to the right

A straight line

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the graph of y = negative square root of (x - 3) look like?

A parabola opening downwards

A straight line

A half-parabola opening to the right

A half-parabola opening to the left

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