What are the asymptotes of the following graph?

  y = ±(1/3)x

Step-by-step explanation:

The asymptotes of this hyperbola will contain the diagonals of the green rectangle. The green rectangle at the center of this hyperbola has corners that have a run from its center of 3 for a rise of ±1, so the slope of the line from its center to the corner is rise/run = ±1/3. The center is at (0, 0), so the equations of the asymptotes are

  y = ±(1/3)x

Part a : Slope is 40 and it interpret the rate of increase of balance in dollars in the account per day.

Part b :  y - 720 = 40(x - 3) ... Point-slope form. 40x - y +600 = 0 ... Standard form. g(x) = 40x + 600 ... Slope-intercept form.

Part c : $880

Step-by-step explanation:

The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:

x  g(x)

0 $600

3 $720

6 $840

Part a : Therefore, the slope of the function will be and it interprets the rate of increase of balance in dollars in the account per day.

Part b : If we denote g(x) = y, then the equation that models the table will be

⇒ y - 720 = 40(x - 3) (1) Point-slope form.

⇒ 40x - y +600 = 0 (2) Standard form.

⇒ y = 40x + 600

⇒ g(x) = 40x + 600 (3) Slope-intercept form.

Part c : From equation (3), the balance in the account after 7 days will be

g(7) = 40(7) + 600 = 280 + 600 = 880 dollars. (Answer)