Question

Which ordered pairs lie on the graph of the exponential function f(x)=−3(x−1)+2?

Select each correct answer.
a) ​​ (4,−25) ​
​b) (1, 1) ​
​c) (0, 0) ​ ​
d) ​​ (−1, 2)

Answer 1

None of the given ordered pairs lie on the graph of the exponential function f(x) = -3(x-1) + 2.

Step-by-step explanation:

The given exponential function is f(x) = -3(x-1) + 2.

To find the ordered pairs that lie on the graph of the exponential function, we need to substitute the given x-values into the function and solve for the corresponding y-values.

1. For option (a) (4, -25):

• f(4) = -3(4-1) + 2 = -3(3) + 2 = -9 + 2 = -7 which is not equal to -25. So, (4, -25) does not lie on the graph.
• For option (b) (1, 1):
  • f(1) = -3(1-1) + 2 = -3(0) + 2 = 0 + 2 = 2 which is not equal to 1. So, (1, 1) does not lie on the graph.
  • For option (c) (0, 0):
    • f(0) = -3(0-1) + 2 = -3(-1) + 2 = 3 + 2 = 5 which is not equal to 0. So, (0, 0) does not lie on the graph.
    • For option (d) (-1, 2):
      • f(-1) = -3(-1-1) + 2 = -3(-2) + 2 = 6 + 2 = 8 which is not equal to 2. So, (-1, 2) does not lie on the graph.

Therefore, none of the given ordered pairs lie on the graph of the exponential function f(x) = -3(x-1) + 2.