To determine which of the given functions satisfies [tex]\( t(4) = 35 \)[/tex], we will evaluate each function at [tex]\( x = 4 \)[/tex] and find out which one equals 35.
Given functions:
1. [tex]\( t(x) = 3x^2 + x - 5 \)[/tex]
2. [tex]\( t(x) = 2x^2 + x - 1 \)[/tex]
3. [tex]\( t(x) = x^3 - 5x - 4 \)[/tex]
4. [tex]\( t(x) = -\infty x^2 + x - 2 \)[/tex]
Ignore the fourth function as it contains an undefined term [tex]\(-\infty x^2\)[/tex].
Evaluate each function at [tex]\( x = 4 \)[/tex]:
### Function 1: [tex]\( t(x) = 3x^2 + x - 5 \)[/tex]
[tex]\[ t(4) = 3(4)^2 + 4 - 5 \][/tex]
[tex]\[ t(4) = 3(16) + 4 - 5 \][/tex]
[tex]\[ t(4) = 48 + 4 - 5 \][/tex]
[tex]\[ t(4) = 47 \][/tex]
### Function 2: [tex]\( t(x) = 2x^2 + x - 1 \)[/tex]
[tex]\[ t(4) = 2(4)^2 + 4 - 1 \][/tex]
[tex]\[ t(4) = 2(16) + 4 - 1 \][/tex]
[tex]\[ t(4) = 32 + 4 - 1 \][/tex]
[tex]\[ t(4) = 35 \][/tex]
### Function 3: [tex]\( t(x) = x^3 - 5x - 4 \)[/tex]
[tex]\[ t(4) = 4^3 - 5(4) - 4 \][/tex]
[tex]\[ t(4) = 64 - 20 - 4 \][/tex]
[tex]\[ t(4) = 40 \][/tex]
Comparing the results, we see the second function [tex]\( t(x) = 2x^2 + x - 1 \)[/tex] satisfies [tex]\( t(4) = 35 \)[/tex].
Thus, the function [tex]\( t(x) = 2x^2 + x - 1 \)[/tex] is the one where [tex]\( t(4) = 35 \)[/tex].
