Question

Consider the exponential function g(x)=1,296x

.

For x=−1.75,−1,−0.25,0,0.25,0.50,0.75,1, find the output values.

a( g(−1.75)= 1/1296,g(−1)=1, g(−0.25)=6, g(0)=1, g(0.25)=36,g(0.50)=216, g(0.75)=1296, g(1)=1296

b) (−1.75 )=1296g(−1.75)=1296, g(−1)=1,0.0625g(−0.25)=0.0625, g(0)=1, g(0.25)=1.5, g(0.50)=36, g(0.75)=81, g(1)=1296

c) g(−1.75)=36, g(−1)=1, g(−0.25)=3, g(0)=1, g(0.25)=6, g(0.50)=12, g(0.75)=24, g(1)=1296

d) 1.750.0007716g(−1.75)=0.0007716, g(−1)=1, 0.046875g(−0.25)=0.046875, g(0)=1, g(0.25)=3, g(0.50)=36,g(0.75)=432, g(1)=1296

Answer 1

The student is to calculate output values for the exponential function g(x)=1,296^x at specified input values. The correct outputs are determined by evaluating the function for each input using a calculator for non-integer exponents.

Step-by-step explanation:

The student is asked to find the output values for various input values of x in the exponential function g(x) = 1,296x. To calculate these values, we must evaluate the function at each given x value. Unfortunately, the options provided (a, b, c, d) contain several accumulated errors, so it's not possible to confirm the correctness of any of those without performing the actual calculations.

Here are the correct output values for the function g(x) = 1,296x:

1. g(-1.75) = 1,296-1.75 ≈ 0.0007716
2. g(-1) = 1,296-1 = 1/1,296 ≈ 0.0007716
3. g(-0.25) = 1,296-0.25 ≈ 0.2362
4. g(0) = 1,2960 = 1
5. g(0.25) = 1,2960.25 ≈ 4.235
6. g(0.50) = 1,2960.50 = 36
7. g(0.75) = 1,2960.75 ≈ 151.7
8. g(1) = 1,2961 = 1,296

Each exponent calculation involves using properties of exponents and potentially a calculator to find decimal approximations for non-integer exponents.