Question

Can someone help me with these questions please?

1. Which function pass through the points (1, 4), (2, 9), and (3, 16)?
y = (x + 1)2
y = (x + 3)2
y = 7x - 5

2. Suppose that after swimming 1 lap in a pool, you can swim 10 laps in an hour. What is an equation that represents the total number of laps you have swam y in terms of the number of hours x?
y(x) = 10 + x
y(x) = 10(x + 1)
y(x) = 10x + 1

3. Is the following an arithmetic sequence? If so, what is the common difference? {4, 2, 0, -2, -4, -6, …}
Yes, d = -2
No
Yes, d = 2

4. Which function has the following graph?

y = -2x + 4 b. y = 2x + 4 c. y =12x + 4

5. What is the slope of the line containing (3, 5) and (2, 7)?
m = 2 b. m = -2 c. m = 125

6. The graph of a line passes through the point (-3, 2) and has a slope of 4. What is an equation of the line?
y = 4x - 10
y = 4x - 11
y = 4x+ 14

7. Which line is parallel to y = 4x - 2?
y = -14x + 3
y = -4x + 5
y = 4x + 5

8. Which system of equations has (2, 3) as a solution?
y = 2x - 1 b. y = 2x + 1 c. y = 4x - 5
y = x + 1 y = x - 1 y = 2x

Answer 1

the first function, y = (x + 1)^2, does pass through the points (1, 4), (2, 9), and (3, 16).

Explanation:

Note that 4, 9 and 16 are squares of 2, 3 and 4. So it's likely that the parent function is of the form f(x) = x^2. Note that f(1) = 1, f(2) = 4, f(3) = 9 and f(4) = 16.

Let's now determine whether these three points satisfy the first given equation, y = (x + 1)^2: Does 4 = (1 + 1)^2? Does 4 = 2^2? YES.

Does 9 = (2 + 1)^2? Does 9 = 3^2? YES

Does 16 = (3 + 1)^2? YES

So the first function, y = (x + 1)^2, does pass through the points (1, 4), (2, 9), and (3, 16).