Questions: Consider the following relation. y=3x-3 Step 1 of 2 : Find four points contained in the inverse. Express your values as an integer or simplified fraction.

Solution Steps

To find the inverse of the function \( y = 3x - 3 \), we need to solve for \( x \) in terms of \( y \).

1. Start with the equation: \( y = 3x - 3 \).
2. Add 3 to both sides: \( y + 3 = 3x \).
3. Divide both sides by 3: \( x = \frac{y + 3}{3} \).

So, the inverse function is \( x = \frac{y + 3}{3} \).

Choose four values for \( x \) and find the corresponding \( y \) values using the original function \( y = 3x - 3 \).

1. Let \( x = 0 \): \( y = 3(0) - 3 = -3 \). Point: \( (0, -3) \).
2. Let \( x = 1 \): \( y = 3(1) - 3 = 0 \). Point: \( (1, 0) \).
3. Let \( x = 2 \): \( y = 3(2) - 3 = 3 \). Point: \( (2, 3) \).
4. Let \( x = -1 \): \( y = 3(-1) - 3 = -6 \). Point: \( (-1, -6) \).

For each point \( (x, y) \) on the original function, the corresponding point on the inverse function is \( (y, x) \).

1. Original point \( (0, -3) \) becomes \( (-3, 0) \).
2. Original point \( (1, 0) \) becomes \( (0, 1) \).
3. Original point \( (2, 3) \) becomes \( (3, 2) \).
4. Original point \( (-1, -6) \) becomes \( (-6, -1) \).

Final Answer