Question

Part A. Given 2x + 7, write an equation whose graph is shifted 3 units to the right.

a) y = 2(x - 3) + 7
b) y = 2(x + 3) + 7
c) y = 2(x - 7) + 3
d) y = 2(x + 7) + 3
Part B. Given y = 2 |x| + 5, write an equation whose graph is reflected, shifted to the left two units, and shifted up four units.
a) y = -2 |x + 2| + 9
b) y = -2 |x - 2| + 9
c) y = 2 |x + 2| + 9
d) y = 2 |x - 2| + 9
Part C. Given y = 3x - 7, write an equation whose wrath is reflected and more steep.
a) y = -3x - 7
b) y = 3x + 7
c) y = -3x + 7
d) y = 3x - 7

Answer 1

The equation for a graph shifted 3 units to the right is y = 2(x - 3) + 7. The equation for a graph reflected, shifted to the left two units, and shifted up four units is y = -2 |x + 2| + 9. The equation for a reflected and steeper graph is y = -3x - 7.

Step-by-step explanation:

Part A. To shift a graph 3 units to the right, we subtract 3 from x inside the equation. Therefore, the equation would be y = 2(x - 3) + 7, which simplifies to y = 2x - 6 + 7.

Part B. To reflect the graph, we negate the entire equation. To shift the graph 2 units to the left, we change the sign of x. To shift it up 4 units, we add 4 to y. Therefore, the equation would be y = -2 |x + 2| + 9.

Part C. To reflect the graph, we negate the coefficient of x. To make it steeper, we increase the coefficient of x. Therefore, the equation would be y = -3x - 7.