Concept explainers
The function
To find a function value
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
College Algebra
- The function f graphed below is defined by a polynomial equation of degree 4 .use the graph to solve the exercises. (a) if f is increasing on an interval then the y-values of the point on the graph _______ as the x-values increase. From the graph of f we see that f is increasing on the interval _______and ________. (b) If f is decreasing on an interval, then the y-values of the points on the graph_____ as the x-values increases. From the graph of f we see that f is decreasing on the interval_____ and______.arrow_forwardThe function f graphed below is defined by a polynomial expression of degree 4. Use the graph of solve the exercises. The domain of the function f is all the _____-values of the points on the graph, and the range is all the corresponding_____-values. From the graph of f we see that the domain of f is the interval ________ and the range of f is the interval ________.arrow_forwardThe function f graphed below is defines by a polynomial expression of degree 4. Use the graph to solve the exercises. (a) A function value f (a) is a local maximum value of f if f (a) is the____ value of f on some open interval containing a. From the graph of f we see that there are two local maximum values of f : One local Maximum is ______, and it occurs when x=2; The other local maximum is ______, and it occurs when x=_______. (b) The function value f (a) is a local minimum value of f if f (a) is the _____ value of f on some open interval containing a.From the graph of f we see that there is one local minimum value of f .The local minimum value is,______ and it occurs when x=______.arrow_forward
- Revenue A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x)=80x0.4x2, where the revenue R(x) is measured in dollars. What is the maximum revenue? and how many units should be manufactured to obtain this maximum?arrow_forwardLocal extrema these exercises involve local maximaand minima of polynomial functions. Graph the function P(x)=(x2)(x4)(x5) and determine how many local extrema it has. If a < b < c, explain why the function P(x)=(xa)(xb)(xc) must have two local extrema-arrow_forwardMaximum Area A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). The perimeter of the window is 16 feet. (a) Write the area A of the window as a function of x. (b) What dimensions produce a window of maximum area?arrow_forward
- Volume of a Box An open box is to constructed from a piece of cardboard 20 cm by 40 cm by cutting squares of side length x from each corner and folding up the sides, as shownin figure. (a) Express the volume V of the box as a function of x. (b) What is the domain of V? (Use the fact that length and volume must be positive.) (c) Draw a graph of the function V, and use it to estimate the maximum volume for such a box.arrow_forward(a) What is the degree of a quadratic function f?What is the standard form of a quadratic function? How do you put a quadratic function into standard form? (b) The quadratic function f(x)=a(xh)2+k is in standard form. The graph of f is a parabola. What is the vertex of the graph of f? How do you determine whether f(h) = k is a minimum or a maximum value? (c) Express f(x)=x2+4x+1 in standard form. Find the vertex of the graph and the maximum or minimum value of f.arrow_forwardVolume of a box A cardboard box has a square base, with each edge of the base having length x inches, as shown in the figure. The total length of all 12 edges of the box is 144 in. (a) Show that the volume of the box is given by the function V(x)=2x2(18x). (b) What is the domain of V? Use the fact that length and volume must be positive. (c) Draw a graph of the function V and use it to estimate the maxim volume for such a box.arrow_forward
- Writing an Equation The graph of a fourth-degree polynomial function y=fx is shown. The equation has 2i as zeros. Write an equation for f.arrow_forwardGraphing Quadratic Functions A quadratic function f is given. (a) Express f in standard form. (b) Find the vertex and x and y-intercept of f . (c) Sketch a graph of f . (d) Find the domain and range of f . f(x)=x2+4x+3arrow_forwardTorricelli's Law Water in a tank will out of a small hole in the bottom when tank is nearly full than when it is nearly empty. According to Torricelli's Law, the Height h(t) of water remaining at time t is a quadratic function of t. A certain tank is filled with and allowed to drain. The height of Water is measured at different times as shown in the table. (a) Find the quadratic polynomial that best fits data. (b) Draw a graph of the polynomial from part(a) together With a scatter plot of the data. (c) Use your graph from part (b) to estimate how long it takes for the tank to drain completely.arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage