source : socratic.org

## What is the domain and range of f(x)= x^2 – 6x + 8?

Domain:

#f(x)# is a quadratic equation and any values of #x# will give a real value of #f(x)#.

The function does not converge to a certain value ie: #f(x)=0# when #x->oo#

Your domain is #{x: -oo<=x<=oo}#.

Range:

Method 1-Use completing the square method:#x^2-6x+8=(x-3)^2-1#Hence you minimum point is #(3,-1)#. It is a minimum point because the graph is a “u” shape (coefficient of #x^2# is positive).

Method 2-Differentiate :#(df(x))/(dx)=2x-6#.

Let#(df(x))/(dx)=0#

Therefore, #x=3# and #f(3)=-1#Minimum point is #(3,-1)#.It is a minimum point because the graph is a “u” shape (coefficient of #x^2# is positive).

Your range takes values between #-1 and oo#

View question – Functions – The upper bound is given when f(x) is $-5$ and g(x) is $-2$, which when multiplied equals $\boxed{10}$.Performing these operations on functions is no more complicated than the notation itself. For instance, when they give you the formulas for two functions and tell you to find the sum, all they're telling you to do is add the two formulas. There's nothing more to this topic than that, other than perhaps some…Air Tutors:Question: Graph and find the domain and range of h(x) = 3x^2 – 5…

Operations on Functions | Purplemath – Functions & Graphing Calculator. Analyze and graph line equations and functions step-by-step. inflection points intercepts inverse laplace inverse laplace partial fractions range slope simplify solve for tangent taylor vertex geometric test alternating test telescoping test pseries test root test.Range is (-11, Infinity). New questions in Math. Q.3 Answer the following questions in one or two sentences (any Two) [M-06]a. Who were the people in Kezia's family?b. What are the Guru's words of wi … sdom?The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. Note 3: We are talking about the domain and range of functions, which have at most one y-value for each x-value, not relations (which can have…

What is the domain and range of the function fx = 3x^2 – 5 – YouTube – Range of a Function For every value given to the independent variable from the domain in a function, we get a corresponding y value. The set of all such If a function is defined by a formula and there is no domain explicitly stated, then it is understood that the domain consists of all real numbers for which…Range: {f(x):-1<=f(x)<=oo} Domain: f(x) is a quadratic equation and any values of x will give a real value of f(x). The function does not converge Let(df(x))/(dx)=0 Therefore, x=3 and f(3)=-1 Minimum point is (3,-1). It is a minimum point because the graph is a "u" shape (coefficient of x^2 is positive).1 Finding the Range of a Function Given a Formula. Find the vertex of the function if it's quadratic. If you're working with a straight line or any function with a polynomial of an odd number, such as f(x) = 6×3+2x + 7, you can skip this step.