Tut 4: Composition of Functions, Sketching Functions, Translations of Functions

CHECK THE LINK BELOW THIS HEADING FOR SOLUTIONS!
Remember to check the corresponding Questions on the memo only

Click here to view the solutions to the question below

2. (a) Sketch the straight line \(2x + 3y + 4\)
(b) Find the equation of the straight line which is perpendicular to the line in (a) and goes through the point (1,1)
(c) Sketch the two lines on the \(xy\)-plane

3. As dry air moves upward, it cools at a rate of about 1°C for each 100 m rises, up to about 12 km.
(a) If the ground temperature is 20°C find a formula for the temperature (T) at height \(h\) (in km.
(b) What range of temperature can be expected if a plane takes off and reaches a maximum height of 5 km.

6. Sketch the graph of \(y = |2x^2 - 3x - 2|\).

7. Sketch the graph of \(y = x^2 - 10x + 28\) by completing the square and applying some translations to the graph of \(y = x^2 \)

9. Given the functions: \(f(x) = 2x^2 = 2\) \(g(x) = \sqrt{x^2 - 4}\) Find the following functions and determine their domains.
(a) \(f + g\)
(b) \(f - g\)
(c) \(f/g\)
(d) \(g/f\)
(e) \(gf\)
(f) \(f \circ g \)

10. Find \(f \circ g \circ h\) and \(h \circ g \circ f\)
\(f(x) = |x| g(x) = \frac{x}{2x - 4} h(x) = \sqrt[3]{x + 2}\)

12. A group of students decides to wrap a length of rope around the earth along the equator. If the radius of the earth at the equator is 6,378km, how long must the rope be ?
If the students now decide to raise the rope so that it is held 1m above the surface of the earth all the way around, how much longer must the rope be ? ( First try to guess the answer, then calculate it)

14. The number \(1.23456789\overline{123456789}\) is a repeating decimal and thus a rational number. Write it in the form \(\frac{p}{q}\) where \(p,q \in \mathcal{Z}\)

Comments

Post a Comment

Popular posts from this blog

Tutorial 2: More Algebra, Inequalities and Absolute values

CHECK THE LINK BELOW THIS HEADING FOR SOLUTIONS! Remember to check the corresponding Questions on the memo only Click here to view the solutions to the question below 1. Solve the equation (a) \(\frac{1}{t-1} + \frac{t}{3} = \frac{1}{3}\) (b) \(\frac{1}{x} = \frac{4}{3x} + 1\) (c) \(\frac{z}{5} = \frac{3}{10}z + 7\) (d) \(r-2[1-3(2r+4)] = 61\) (e) \((t-4)^{2} = (t+4)^{2} + 32\) (f) \(\frac{2}{3}x - \frac{1}{4} = \frac{1}{6}x - \frac{1}{9}\) (g) \(\frac{4}{x-1} + \frac{2}{x + 1} = \frac{35}{x^2 - 1}\) (h) \((\frac{1}{x-1} 2 \frac{2}{x^2}\) (i) \(\sqrt{2x + 1} + 1 = x\) (j) \(\sqrt{\sqrt{x-5}+x} = 5\) (k) \(4(x + 1)^{\frac{1}{2}} - 5(x + 1)^{\frac{3}{2}} + (x + 1)^{\frac{5}{2}} = 0\) 2. Solve the inequality. Express the solution in interval form and illustrate the solution set on the real number line. (a) \(4-3x \leq -(1+8x)\) (b) \( \frac{2x+1}{x-5} \leq 3\) (c) \( \frac{(x-1)^2}{(x+1)(x+3)}\) (d) \
Read more

Tutorial 1: Pre-Calculus: Sets and Basic Algebra Involving Simplifying and Rationalizing Expressions

Quick Solutions to Pre-Calculus: Sets and Basic Algebra Involving Simplifying and Rationalizing Expressions This how-to blog is s resource of QUICK MATH SOLUTIONS for students who wants to find a quick way to pass their first year of college or university MATHEMATICS without having to worry about the theory bull they force you to remember. SO LETS JUMP IN TO IT! AND CHECK THE LINK BELOW THIS HEADING! Click here to view the solutions to the question below Question 1. Use the roster method to name each set: 1. \(A=\{x \mid x \mbox{ is an integer and } 1<= x <= 8 \}\) 2. \(B=\{y \mid y \mbox{ is an integer and } -5<= y <= 0 \}\) Question 2. Use the builder notation to name each set: 1. A=\(\{-1,0,1,2\}\) 2. B=\(\{10,11,12,13,\dots\}\) 3. C=\(\{10,20,30,40,\dots\}\) Question 3. Place \(\subset\), \(\supset\) or = in each blank to make a true sentence. 1. A=\(\{8,9\}\do
Read more