First, give the technology formula for the given function and then use technology to evaluate the function for the given values of x. (Round your answers to four decimal places.)
r(x) = 4x2 + 1/4x2 − 1; x = −1, 0, 1, ..., 9
a)(4x^2 − 1)/(4x^2 + 1)
b)(4x + 1)^2/(4x − 1)^2
c)(4*x^2 + 1)/(4*x^2 − 1)
d)(4*x*2 + 1)/(4*x*2 − 1)
r(−1)=
r(0)=
r(1)=
r(2)=
r(3)=
r(4)=
r(5)=
r(6)=
r(7)=
r(8)=
r(9)=
Thank You.
I'm sorry, its r(x) = (4x^2 + 1)/(4x^2 − 1); x = −1, 0, 1, ..., 9
The correct technology formula for the given function r(x) = 4x^2 + 1/4x^2 - 1 is option c) (4*x^2 + 1)/(4*x^2 - 1).
Using technology to evaluate the function for the given values of x:
r(-1) = (4*(-1)^2 + 1)/(4*(-1)^2 - 1) = (4 + 1)/(4 - 1) = 5/3
r(0) = (4*0^2 + 1)/(4*0^2 - 1) = (1)/(0 - 1) = -1
r(1) = (4*1^2 + 1)/(4*1^2 - 1) = (4 + 1)/(4 - 1) = 5/3
r(2) = (4*2^2 + 1)/(4*2^2 - 1) = (16 + 1)/(16 - 1) = 17/15
r(3) = (4*3^2 + 1)/(4*3^2 - 1) = (36 + 1)/(36 - 1) = 37/35
r(4) = (4*4^2 + 1)/(4*4^2 - 1) = (64 + 1)/(64 - 1) = 65/63
r(5) = (4*5^2 + 1)/(4*5^2 - 1) = (100 + 1)/(100 - 1) = 101/99
r(6) = (4*6^2 + 1)/(4*6^2 - 1) = (144 + 1)/(144 - 1) = 145/143
r(7) = (4*7^2 + 1)/(4*7^2 - 1) = (196 + 1)/(196 - 1) = 197/195
r(8) = (4*8^2 + 1)/(4*8^2 - 1) = (256 + 1)/(256 - 1) = 257/255
r(9) = (4*9^2 + 1)/(4*9^2 - 1) = (324 + 1)/(324 - 1) = 325/323
Therefore, the evaluated values of the function r(x) for x = -1, 0, 1, ..., 9 are as follows:
r(-1) = 5/3
r(0) = -1
r(1) = 5/3
r(2) = 17/15
r(3) = 37/35
r(4) = 65/63
r(5) = 101/99
r(6) = 145/143
r(7) = 197/195
r(8) = 257/255
r(9) = 325/323
You're welcome!
To evaluate the function r(x) = 4x^2 + 1/(4x^2 - 1) for the given values of x, we can use a scientific calculator or any software with mathematical capabilities.
The correct formula for the given function is c) (4*x^2 + 1)/(4*x^2 - 1).
We can substitute the values of x into the formula and evaluate the function using a calculator or software as follows:
a) r(-1) = (4*(-1)^2 + 1)/(4*(-1)^2 - 1) = (4 + 1)/(4 - 1) = 5/3
b) r(0) = (4*(0)^2 + 1)/(4*(0)^2 - 1) = (1)/(0 - 1) = -1
c) r(1) = (4*(1)^2 + 1)/(4*(1)^2 - 1) = (4 + 1)/(4 - 1) = 5/3
d) r(2) = (4*(2)^2 + 1)/(4*(2)^2 - 1) = (16 + 1)/(16 - 1) = 17/15
e) r(3) = (4*(3)^2 + 1)/(4*(3)^2 - 1) = (36 + 1)/(36 - 1) = 37/35
f) r(4) = (4*(4)^2 + 1)/(4*(4)^2 - 1) = (64 + 1)/(64 - 1) = 65/63
g) r(5) = (4*(5)^2 + 1)/(4*(5)^2 - 1) = (100 + 1)/(100 - 1) = 101/99
h) r(6) = (4*(6)^2 + 1)/(4*(6)^2 - 1) = (144 + 1)/(144 - 1) = 145/143
i) r(7) = (4*(7)^2 + 1)/(4*(7)^2 - 1) = (196 + 1)/(196 - 1) = 197/195
j) r(8) = (4*(8)^2 + 1)/(4*(8)^2 - 1) = (256 + 1)/(256 - 1) = 257/255
k) r(9) = (4*(9)^2 + 1)/(4*(9)^2 - 1) = (324 + 1)/(324 - 1) = 325/323
Overall, the values for r(x) for x = -1 to 9 (inclusive) are:
r(-1) = 5/3
r(0) = -1
r(1) = 5/3
r(2) = 17/15
r(3) = 37/35
r(4) = 65/63
r(5) = 101/99
r(6) = 145/143
r(7) = 197/195
r(8) = 257/255
r(9) = 325/323