MAT 1001 College Algebra COMPLETED EXAM 2026-2027 10pages

1. What is the domain and range of the function f(x) = 2x - 3 / (x + 1)? Answer: The domain of f(x) is the set of all real numbers except -1, since -1 would make the denominator zero and the function undefined. The range of f(x) is the set of all real numbers except 2, since 2 is a horizontal asymptote of the function. To find the horizontal asymptote, we can divide both the numerator and denominator by x and take the limit as x approaches infinity. We get lim x->inf (2x - 3) / (x + 1) = lim x->inf 2 - 3/x / (1 + 1/x) = 2 - 0 / (1 + 0) = 2. 2. How do you solve a system of linear equations using the substitution method? Give an example with your solution. Answer: To solve a system of linear equations using the substitution method, we first isolate one variable in one equation and then substitute it into the other equation. This gives us a single equation with one variable that we can solve. Then we can plug the value of that variable back into either equation to find the value of the other variable. For example, consider the system: x + y = 5 3x - y = 7 We can isolate y in the first equation by subtracting x from both sides: y = 5 - x Then we can substitute this expression for y into the second equation: 3x - (5 - x) = 7 Simplifying and solving for x, we get: 4x - 5 = 7 4x = 12