question\nuse graphing technology to find the domain of the function $f(x) = -x^2 + 4x - 5$.
question\nuse graphing technology to find the domain of the function $f(x) = -x^2 + 4x - 5$.
Answer
Explanation:
Step1: Recall the function type
The function ( f(x) = -x^2 + 4x - 5 ) is a quadratic function. The general form of a quadratic function is ( f(x)=ax^{2}+bx + c ), where ( a=- 1), ( b = 4), ( c=-5 ).
Step2: Analyze the domain of a quadratic function
For a quadratic function (a polynomial function of degree 2), the domain of a polynomial function is all real numbers because there are no restrictions on the values of ( x ) that we can plug into the function (we don't have division by zero, square roots of negative numbers in the real - valued case for a polynomial, etc.). When we use graphing technology to graph ( y=-x^{2}+4x - 5 ), we will see that the parabola (the graph of the quadratic function) extends infinitely to the left and to the right along the ( x ) - axis, meaning that ( x ) can take on any real - number value.