Square Root and Inverse Variation Functions Review

Front

What is the starting point of the function \( f(x) = \sqrt{x} - 2 \)?

Back

(0, -2)

Front

What is the starting point of the graph of the radical function?

Back

(-4, -2)

Front

If \( y \) varies jointly as \( x \) and \( z \), and \( y = -180 \) when \( z = 15 \) and \( x = -3 \), what is \( y \) when \( x = 7 \) and \( z = -5 \)?

Back

-140

Front

Solve for \( x \): \( 7 + x^{3/2} = 71 \)

Back

16

Front

The number of hours to paint a house varies inversely with the number of painters. If a 2400-square foot house can be painted in 27 hours by 6 painters, how many painters are needed to paint the house in 18 hours?

Back

9 painters

Front

Define the square root function.

Back

The square root function is defined as \( f(x) = \sqrt{x} \), which returns the non-negative value whose square is \( x \).

Front

What is inverse variation?

Back

Inverse variation describes a relationship where one variable increases as the other decreases, typically expressed as \( y = \frac{k}{x} \) for some constant \( k \).

Front

What is the domain of the function \( f(x) = \sqrt{x} \)?

Back

The domain is \( [0, \infty) \) because the square root is only defined for non-negative numbers.

Front

What is the range of the function \( f(x) = \sqrt{x} - 2 \)?

Back

The range is \( [-2, \infty) \) because the minimum value occurs at \( x = 0 \).

Front

How do you find the starting point of a radical function?

Back

The starting point is found by evaluating the function at its minimum input value, typically where the expression under the square root is zero.