1 - Amosam
... If g(x) = x3 + x2 and f(x) = 2x – 5, then h(x) = f(g(x)) = f(x3 + x2) = 2(x3 + x2) – 5 The range of g(x) becomes the domain of f(x). For example in the above function, if the domain for g(x) is 2, the range value becomes 12. This becomes the domain for f(x), producing a range value of 19. We can say ...
... If g(x) = x3 + x2 and f(x) = 2x – 5, then h(x) = f(g(x)) = f(x3 + x2) = 2(x3 + x2) – 5 The range of g(x) becomes the domain of f(x). For example in the above function, if the domain for g(x) is 2, the range value becomes 12. This becomes the domain for f(x), producing a range value of 19. We can say ...
Module 8 Study Guide - Valley Oaks Charter School Tehachapi
... and from work. a. Choose variables to represent the unknown quantities in this problem. State which variable is the independent variable and which is the dependent variable, and give the unit of measurement for each. b. Using unit analysis as a guide, write a function that models the total amount of ...
... and from work. a. Choose variables to represent the unknown quantities in this problem. State which variable is the independent variable and which is the dependent variable, and give the unit of measurement for each. b. Using unit analysis as a guide, write a function that models the total amount of ...
USACAS_withScreenShots - Michael Buescher`s Home Page
... the following True or False: –Multiplication distributes over addition and subtraction –Division distributes over addition and subtraction –Exponents distribute over addition and subtraction –Roots distribute over addition and subtraction ...
... the following True or False: –Multiplication distributes over addition and subtraction –Division distributes over addition and subtraction –Exponents distribute over addition and subtraction –Roots distribute over addition and subtraction ...
Chapter 2 Formulas and Definitions
... 3. Find the zeros of the numerator (if any) by setting the numerator equal to zero. Then plot the corresponding x-intercepts. 4. Find the zeros of the denominator (if any) by setting the denominator equal to zero. then sketch the corresponding vertical asymptotes using dashed vertical lines and plot ...
... 3. Find the zeros of the numerator (if any) by setting the numerator equal to zero. Then plot the corresponding x-intercepts. 4. Find the zeros of the denominator (if any) by setting the denominator equal to zero. then sketch the corresponding vertical asymptotes using dashed vertical lines and plot ...
Exponential Functions
... more and more negative. In both cases, neither graph touches the x-axis, even though both functions are approaching zero as x becomes very negative. This is our first example of a horizontal asymptote, which is illustrated in a graph by the curve of that graph getting closer and closer to a horizont ...
... more and more negative. In both cases, neither graph touches the x-axis, even though both functions are approaching zero as x becomes very negative. This is our first example of a horizontal asymptote, which is illustrated in a graph by the curve of that graph getting closer and closer to a horizont ...
Unit 5 Test Name: Part 2 (Exponential Functions) Block: ______ A
... Directions: Given the following situation, label each statement as true or false. If it is false, correct the statement to make it true. The population of a town over the past 10 years can be represented by the equation: y = 2450(1.07)x _____ 18. The initial population was 2400. ...
... Directions: Given the following situation, label each statement as true or false. If it is false, correct the statement to make it true. The population of a town over the past 10 years can be represented by the equation: y = 2450(1.07)x _____ 18. The initial population was 2400. ...
Section 1.5
... By factoring the denominator as you can see that the denominator is 0 at x = –1 and x = 1. Also, because the numerator is not 0 at these two points, you can apply Theorem 1.14 to conclude that the graph of f has two vertical asymptotes, as shown in figure 1.43(b). Figure 1.43(b) ...
... By factoring the denominator as you can see that the denominator is 0 at x = –1 and x = 1. Also, because the numerator is not 0 at these two points, you can apply Theorem 1.14 to conclude that the graph of f has two vertical asymptotes, as shown in figure 1.43(b). Figure 1.43(b) ...
Test II Form C
... parking. If the developer has 500 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? (9 points) ...
... parking. If the developer has 500 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed? (9 points) ...
Chapter 10 Study Sheet
... Chapter 8 Study Sheet I. Exponential Functions: A. An exponential function has the form y = __________. B. If the function f(x) = abx has a > 0 and b > 1, then it is an example of an exponential ______________ function. C. If the function f(x) = abx has a > 0 and 0 < b < 1, then it is an example of ...
... Chapter 8 Study Sheet I. Exponential Functions: A. An exponential function has the form y = __________. B. If the function f(x) = abx has a > 0 and b > 1, then it is an example of an exponential ______________ function. C. If the function f(x) = abx has a > 0 and 0 < b < 1, then it is an example of ...
7.4a Linear Reciprocal Functions
... (Big -> Small) When f(x) > 1, the reciprocal function approaches the horizontal asymptote (Small -> Big) When 0 < f(x) < 1, the reciprocal function approaches the vertical asymptote ...
... (Big -> Small) When f(x) > 1, the reciprocal function approaches the horizontal asymptote (Small -> Big) When 0 < f(x) < 1, the reciprocal function approaches the vertical asymptote ...
Chapter 4 Review Worksheet
... 5) Let f ( x) ( x 3)2 ( x 4)5 . Find the x and y intercepts, graph the excluded regions and sketch the graph of f. (hint: use a sign chart to find excluded regions) Problems 6 -8: Find the x and y intercepts, and vertical and horizontal asymptotes and graph f. Does the graph cross the horizont ...
... 5) Let f ( x) ( x 3)2 ( x 4)5 . Find the x and y intercepts, graph the excluded regions and sketch the graph of f. (hint: use a sign chart to find excluded regions) Problems 6 -8: Find the x and y intercepts, and vertical and horizontal asymptotes and graph f. Does the graph cross the horizont ...
Rational Function Analysis 1. Reduce R x to lowest terms. 2
... 1. Reduce R ( x ) to lowest terms. 2. Determine the x-intercepts by setting the numerator equal to zero. 3. Determine the y-intercepts by finding R ( 0 ) . 4. Determine the equation (x = ___ ) of all vertical asymptotes by setting the denominator equal to zero. Graphs will never cross the vertical a ...
... 1. Reduce R ( x ) to lowest terms. 2. Determine the x-intercepts by setting the numerator equal to zero. 3. Determine the y-intercepts by finding R ( 0 ) . 4. Determine the equation (x = ___ ) of all vertical asymptotes by setting the denominator equal to zero. Graphs will never cross the vertical a ...
Asymptote
In analytic geometry, an asymptote (/ˈæsɪmptoʊt/) of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. Some sources include the requirement that the curve may not cross the line infinitely often, but this is unusual for modern authors. In some contexts, such as algebraic geometry, an asymptote is defined as a line which is tangent to a curve at infinity.The word asymptote is derived from the Greek ἀσύμπτωτος (asumptōtos) which means ""not falling together"", from ἀ priv. + σύν ""together"" + πτωτ-ός ""fallen"". The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve.There are potentially three kinds of asymptotes: horizontal, vertical and oblique asymptotes. For curves given by the graph of a function y = ƒ(x), horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to +∞ or −∞. Vertical asymptotes are vertical lines near which the function grows without bound.More generally, one curve is a curvilinear asymptote of another (as opposed to a linear asymptote) if the distance between the two curves tends to zero as they tend to infinity, although the term asymptote by itself is usually reserved for linear asymptotes.Asymptotes convey information about the behavior of curves in the large, and determining the asymptotes of a function is an important step in sketching its graph. The study of asymptotes of functions, construed in a broad sense, forms a part of the subject of asymptotic analysis.