is this a function?

Question

(-3, 4) (-2, 3) (0, 1) (-2, 1) (-4, -3)

Answer 1

To determine if a set of ordered pairs represents a function, we need to check if each input (the first element of each pair) is associated with exactly one output (the second element of each pair).

In the given set of ordered pairs:

• (-3, 4)
• (-2, 3)
• (0, 1)
• (-2, 1)
• (-4, -3)

We can see that the first element -2 appears in two pairs: (-2, 3) and (-2, 1). Since -2 is associated with two different outputs (3 and 1), this violates the definition of a function.

Therefore, this set of ordered pairs does not represent a function.

Answer 2

find the range of the function with the given domain.
f(x)=4x-2
Domain: {2, -1, 0, 1, 2}

Answer 3

To find the range of the function \( f(x) = 4x - 2 \) given the specified domain \( {2, -1, 0, 1, 2} \), we will evaluate \( f(x) \) for each value in the domain.

1. For \( x = 2 \): \[ f(2) = 4(2) - 2 = 8 - 2 = 6 \]

2. For \( x = -1 \): \[ f(-1) = 4(-1) - 2 = -4 - 2 = -6 \]

3. For \( x = 0 \): \[ f(0) = 4(0) - 2 = 0 - 2 = -2 \]

4. For \( x = 1 \): \[ f(1) = 4(1) - 2 = 4 - 2 = 2 \]

5. For \( x = 2 \) again (since it appears twice in the domain): \[ f(2) = 4(2) - 2 = 6 \quad (\text{already calculated}) \]

Now, we compile the outputs:

• \( f(2) = 6 \)
• \( f(-1) = -6 \)
• \( f(0) = -2 \)
• \( f(1) = 2 \)

Thus, the outputs from the function for the given domain are: \[ {-6, -2, 2, 6} \]

Therefore, the range of the function \( f(x) = 4x - 2 \) given the domain \( {2, -1, 0, 1, 2} \) is: \[ {-6, -2, 2, 6} \]

Answer 4

what is the slope and y intercept of y=4x-12

Answer 5

The equation \( y = 4x - 12 \) is in slope-intercept form, which is generally written as \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

From the equation \( y = 4x - 12 \):

• Slope (m): The coefficient of \( x \) is \( 4 \). So, the slope is \( 4 \).

• Y-intercept (b): The constant term is \(-12\). Thus, the y-intercept is \(-12\).

Summary:

• Slope: \( 4 \)
• Y-intercept: \( -12 \) (This means the line intersects the y-axis at the point \( (0, -12) \)).

Answer 6

write an equation in point slope form for the given line. Point A is at (-4,4) and point B is at (-2,0)

Answer 7

To write an equation in point-slope form using the two points \( A(-4, 4) \) and \( B(-2, 0) \), we first need to find the slope of the line that passes through these points.

Step 1: Calculate the slope (m)

The slope \( m \) is calculated using the formula:

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

Using the points \( A(-4, 4) \) (where \( x_1 = -4, y_1 = 4 \)) and \( B(-2, 0) \) (where \( x_2 = -2, y_2 = 0 \)):

\[ m = \frac{0 - 4}{-2 - (-4)} = \frac{-4}{-2 + 4} = \frac{-4}{2} = -2 \]

Step 2: Use point-slope form

The point-slope form of a line is given by:

\[ y - y_1 = m(x - x_1) \]

We can use either point \( A(-4, 4) \) or point \( B(-2, 0) \). Let's use point \( A \):

• \( m = -2 \)
• \( (x_1, y_1) = (-4, 4) \)

Substituting into the point-slope form:

\[ y - 4 = -2(x - (-4)) \]

This simplifies to:

\[ y - 4 = -2(x + 4) \]

Alternatively, using point \( B(-2, 0) \):

• \( (x_1, y_1) = (-2, 0) \)

Substituting gives:

\[ y - 0 = -2(x - (-2)) \]

Which simplifies to:

\[ y = -2(x + 2) \]

Final Equation

Thus, the equation in point-slope form for the line passing through points \( A \) and \( B \) can be written as:

1. Using point \( A \): \[ y - 4 = -2(x + 4) \]

2. Using point \( B \): \[ y = -2(x + 2) \]

Both forms are valid and represent the same line.