Write down the rational function f(x) = 3x/x^2. Write down the polynomial in the denominator and equate it to 0, "x^2 =0." Solve for the variable x. Observe that the number 0 is the only value for x that will make this equation true. Conclude that the domain of f(x) is all real numbers except the number 0, since f(0) = 3*0/0^2 = 0/0 and dividing by 0 produces an undefined number (which is not a real number).
Write down the rational function f(x) = x/(x-3). Write the polynomial in the denominator and equate it to 0, "x-3 =0." Solve for the variable x. Observe that the number 3 is the only value for x that will make this equation true. Conclude that the domain of f(x) is all real numbers except the number 3, since f(3) = 3/(3-3) = 3/0 and dividing by 0 produces an undefined number.
Record the rational function f(x) = (x^2 + 3)/(x + 10). Write down the polynomial in the denominator and equate it to 0, "x + 10 =0." Solve for the variable x. Observe that the number -10, is the only value for x that will make this equation true. Conclude that the domain of f(x) is all real numbers except the number -10, since f(-10) = 103/(-10 + 10) = 103/0 and dividing by 0 produces an undefined number.
Write the rational function f(x) = (x^2 + 3)/(x^2 -1). Write down the polynomial in the denominator and equate it to 0, "x^2 - 1 =0." Solve for the variable x. Observe that the number -1 and the number 1 are the only two values that will make this equation true. Conclude that the domain of f(x) is all real numbers except the numbers 1 and -1 since f(1) = 4/(1 -1) = 1/0 and f(-1) = 4/(1 -1) = 1/0 and dividing by 0 produces undefined numbers.