Answer:
Point (1 , 0.75) lies on the graph of the function ⇒ last answer
Explanation:
* Lets revise the exponential function
- An exponential function with base b is defined by f (x) = ab^x
where a ≠0, b > 0 , b ≠1, and x is any real number.
- The base, b, is constant and the exponent, x, is a variable.
- The graph of it in the attached figure
- Features (for this graph):
• The domain is all Real numbers.
• The range is all positive real numbers (not zero).
• The y-intercept at (0 , 1.5). Remember any number to
the power of zero is 1.
• Because 0 < b < 1, the graph decreases (b = 1/2)
* Now lets check which point lies on the graph
- Substitute the value of x of the point, in the function
- If the answer is the same as y, then the point lies on the graph of
the function
∵ y = 1.5(1/2)^x
∵ x = -3
∴ y = 1.5(1/2)^(-3) = 187.5 ≠ 1
∴ Point (-3 , 1) does not lie on the graph of the function
∵ x = 2
∴ y = 1.5(1/2)² = 3/8 ≠ 5
∴ Point (2 , 5) does not lie on the graph of the function
∵ x = -2
∴ y = 1.5(1/2)^-2 = 6 ≠ 3
∴ Point (-2 , 3) does not lie on the graph of the function
∵ x = 1
∴ y = 1.5(1/2)^1 = 0.75
∴ Point (1 , 0.75) lies on the graph of the function