Questions: Find two ordered pairs of the given function. a) y = sqrt(4-x) b) y = x^2 + x - 6 c) y = 10x - 7 d) y = x^2 / (x - 1)

Transcript text: 5. Find two ordered pairs of the given function. a) $y=\sqrt{4-x}$ b) $y=x^{2}+x-6$ c) $y=10 x-7$ d) $y=\frac{x^{2}}{x-1}$

Solution

Solution Steps

To find ordered pairs for a given function, we can choose arbitrary values for $ x $ and then compute the corresponding $ y $ values using the function's equation. This will give us the ordered pairs $(x, y)$.

Step 1: Find Ordered Pairs for $ y = \sqrt{4 - x} $

We chose $ x = 0 $ and $ x = 1 $ to find the corresponding $ y $ values:

For $ x = 0 $: \[ y = \sqrt{4 - 0} = \sqrt{4} = 2.0 \]
For $ x = 1 $: \[ y = \sqrt{4 - 1} = \sqrt{3} \approx 1.7321 \] Thus, the ordered pairs are $ (0, 2.0) $ and $ (1, 1.7321) $.

Step 2: Find Ordered Pairs for $ y = x^2 + x - 6 $

Again, using $ x = 0 $ and $ x = 1 $:

For $ x = 0 $: \[ y = 0^2 + 0 - 6 = -6 \]
For $ x = 1 $: \[ y = 1^2 + 1 - 6 = 1 + 1 - 6 = -4 \] Thus, the ordered pairs are $ (0, -6) $ and $ (1, -4) $.

Step 3: Find Ordered Pairs for $ y = 10x - 7 $

Using the same $ x $ values:

For $ x = 0 $: \[ y = 10 \cdot 0 - 7 = -7 \]
For $ x = 1 $: \[ y = 10 \cdot 1 - 7 = 10 - 7 = 3 \] Thus, the ordered pairs are $ (0, -7) $ and $ (1, 3) $.