Determine if the relation y = 4x - 1 is a function by first graphing the relation, then applying the vertical line test. Enter 1 of the relation is a function. Enter 2 if the relation is not a function

Answer 1

To determine if the relation \( y = 4x - 1 \) is a function, we can analyze its graph and also apply the vertical line test.

1. The equation \( y = 4x - 1 \) represents a linear function, which can be graphed as a straight line.
2. To apply the vertical line test, we can consider the definition: a relation is a function if no vertical line intersects the graph more than once.

Since the graph of \( y = 4x - 1 \) is a straight line, any vertical line will intersect it at exactly one point. Therefore, it passes the vertical line test.

Thus, the relation \( y = 4x - 1 \) is a function.

You should enter 1, as the relation is a function.

Answer 2

Determine if 7x² + y = 5 is a linear or nonlinear function

Answer 3

To determine whether the equation \( 7x^2 + y = 5 \) represents a linear or nonlinear function, we can analyze the form of the equation.

A linear function can be expressed in the standard form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. In a linear function, the highest power of the variable \( x \) is 1.

In the equation \( 7x^2 + y = 5 \), the term \( 7x^2 \) has \( x \) raised to the power of 2, which indicates that this is a quadratic term.

To express this equation in the form of \( y \):

\[ y = -7x^2 + 5 \]

Since the highest power of \( x \) in this expression is 2, the relation is not linear.

Therefore, the function represented by the equation \( 7x^2 + y = 5 \) is nonlinear.

Answer 4

Use the image to answer this question.
The dots are at 0, 3 and 1, 5
Determine if the given graph of the function y = -2/5x + 3
Enter 1 if yes enter 2 if no

Answer 5

To determine if the line represented by the function \( y = -\frac{2}{5}x + 3 \) passes through the points \( (0, 3) \) and \( (1, 5) \), we can evaluate the function at these x-values.

1. Evaluate at \( x = 0 \):

\[ y = -\frac{2}{5}(0) + 3 = 3 \]

This gives the point \( (0, 3) \), which is on the line.

2. Evaluate at \( x = 1 \):

\[ y = -\frac{2}{5}(1) + 3 = -\frac{2}{5} + 3 = \frac{15}{5} - \frac{2}{5} = \frac{13}{5} = 2.6 \]

So for \( x = 1 \), the value of \( y \) is \( 2.6 \), which does not match with the point \( (1, 5) \).

Since the function passes through \( (0, 3) \) but does not pass through \( (1, 5) \), the answer is 2 (no).

Answer 6

It passes through both

Answer 7

Let's clarify and check both points again.

1. Point (0, 3):

   • Substituting \( x = 0 \) into the equation \( y = -\frac{2}{5}x + 3 \): \[ y = -\frac{2}{5}(0) + 3 = 3 \]
   • This means that the point \( (0, 3) \) is on the line.

2. Point (1, 5):

   • Substituting \( x = 1 \) into the equation: \[ y = -\frac{2}{5}(1) + 3 = -\frac{2}{5} + 3 = -\frac{2}{5} + \frac{15}{5} = \frac{13}{5} = 2.6 \]
   • This means that the point \( (1, 5) \) is not on the line.

So upon checking, the line does pass through \( (0, 3) \) but does not pass through \( (1, 5) \).

Therefore, if you are stating that it passes through both points, this is incorrect with respect to the function \( y = -\frac{2}{5}x + 3 \). The correct evaluation remains:

• Answer: 2 (no).

If you have further information or a different graph, please provide it for re-evaluation!

Answer 8

Determine the initial value and rate of change in the following description

Last year, Joshua's tomato plant reached a maximum height of 2 feet. He is growing another tomato plant this year and he's tracking the growth. The plants height today is 10 inches, and it grows 1.7 inches each day.

The initial value is b = __ and the rate of change is m = __

Answer 9

To determine the initial value and rate of change from the given description, we can break it down as follows:

1. Initial Value (b):

   • The initial value in this context usually refers to the starting point of the plant's height before any growth happens. Since the height of the new tomato plant today is given as 10 inches, we use this height as the initial value.
   • Thus, the initial value \( b = 10 \) inches.

2. Rate of Change (m):

   • The rate of change refers to how much the plant's height increases each day, which is given as 1.7 inches per day.
   • Therefore, the rate of change \( m = 1.7 \) inches per day.

So, to summarize:

• The initial value is \( b = 10 \) inches.
• The rate of change is \( m = 1.7 \) inches per day.

Answer 10

Use the table to answer this question
The table shows x and y with 22 and 25 being under y and 2 and 8 under x
Determine the rate of change and the initial value of the linear function given here as a table of values

The rate of change is m = __ and the initial value is b = __

Answer 11

To determine the rate of change and the initial value from the provided table:

• We have two points based on the values:
  • Point 1: \( (2, 22) \)
  • Point 2: \( (8, 25) \)

Step 1: Calculate the Rate of Change (m)

The rate of change \( m \) can be calculated using the formula:

\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the values from the points:

• \( (x_1, y_1) = (2, 22) \)
• \( (x_2, y_2) = (8, 25) \)

\[ m = \frac{25 - 22}{8 - 2} = \frac{3}{6} = \frac{1}{2} \]

Step 2: Determine the Initial Value (b)

The initial value \( b \) typically refers to the value of \( y \) when \( x = 0 \). However, we can express the linear function in the slope-intercept form \( y = mx + b \).

We have the slope \( m = \frac{1}{2} \) and we can use one of the points to find \( b \). Let’s use \( (2, 22) \):

\[ y = mx + b \]

Substituting the values:

\[ 22 = \frac{1}{2}(2) + b \]

\[ 22 = 1 + b \]

\[ b = 22 - 1 = 21 \]

Summary

• The rate of change is \( m = \frac{1}{2} \).
• The initial value is \( b = 21 \).