Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.
x 1 3 5 10
y 4 12 20 40
A. direct variation; y equals 4 times x
B. direct variation; y equals one-fourth x
C. inverse variation; x times y equals 4
D. inverse variation; x times y equals one fourth
B. direct variation; y equals one-fourth x
What are the excluded values of the function?
y equals 3 over the quantity 4 times x plus 64
A. x = 0
B. x equals negative 64
C. x equals negative 16
D. x equals negative 8
B. x equals negative 64
To determine whether the data in the table represents a direct variation or an inverse variation, we need to analyze the relationship between x and y.
Direct variation occurs when y is directly proportional to x. In this case, as x increases, so does y.
Inverse variation occurs when the product of x and y is constant. Inverse variation shows that as x increases, y decreases and vice versa.
Let's check if the data in the table exhibits direct or inverse variation.
If we calculate the ratios of y to x, we get:
y / x = 4 / 1 = 4
y / x = 12 / 3 = 4
y / x = 20 / 5 = 4
y / x = 40 / 10 = 4
Since the ratio y / x is constant (4) for all values of x and y, we can conclude that the data represents a direct variation.
Thus, the equation to model the data in the table is:
y = 4x
Therefore, the correct answer is: A. direct variation; y equals 4 times x.