3. 2. What is the sum h(x) + g(x) if h(x) = 5x – 1 and g(x) = 3x2 + 6x – 7 ?
4. 3. If F(x)= 2x + 3 and G(x) = 5x – 4, what is the composite function G(F(x))?
5. 4. What is the domain of the square root function ? DOMAIN The set of all possible values for x, OR The x-coordinates of the points of the graph of the function 2 ways to analyze: 1.) Knowing the graph of the function 2.) Using the given equation of the function
6. The graph of What are the x-coordinates of the points on the graph? DOMAIN
7. The graph of DOMAIN of is at x=5 Courtesy of Wolfram Alpha: www/wolframalpha.com GENERAL EQUATION: h=horizontal shift
9. 6. Find the inverse of the function . HOW TO GET 1.) Use y for “f(x)”. 2.) Switch x and y. 3.) Isolate y. 4.) This new y will be your
10. 7. Which of the following is NOT divisible by (x – 1) ? 3 Ways to answer: 1.) Using LONG division. 2.) Using SYNTHETIC division. 3.) Using the REMAINDER THEOREM. Remainder Theorem: Therefore, is divisible by (x - 1).
11. 8. What are the roots of the function ? ROOTS – also known as the x-coordinates of the x-intercepts, OR the solutions to the equation if h( x ) were equal 0. HOW DO WE GET THE x-intercepts? Let y = 0, meaning let h( x ) = 0.
12. Which is the correct set of roots of f( x )? x = -3, 0 and 5 OR x = -5, 0 and 3
13. 9. What is the equation of the line that passes through (5, -6) and is perpendicular to the line whose equation is ? Point (5, -6) is a point on the line we are looking for. Perpendicular means that the slopes of and the unknown line are NEGATIVE RECIPROCALS of each other.
16. 11. Given the function : Find the vertex of the parabola. 2 ways: 1.) Vertex-form of the quadratic equation. 2.) Use the vertex formula.
17. 11.b. Find the domain and range. Domain – set of all real numbers: Range – based on 2 things: 1.) the y-coordinate of the VERTEX of the parabola. 2.) the direction where the parabola is opening leading coefficient. Therefore, the range is
20. RECALL: Pythagorean Theorem If side a = 5 cm. and side c = 13 cm., what is the length of side b? c a b where a and b are the LEGS, and c is the hypotenuse.
21. RECALL: The 30-60-90 TRIANGLE THEOREMS 60 c a 30 b The side opposite 30 degrees will have a length of ½ of the length of the longest side (hypotenuse). The side opposite 60 degrees will be times the length of the longest side.
22. RECALL: THE 45-45-90 TRIANGLE a a c In terms of the sides, what kind of triangle is the 45-45-90 triangle? The length of the longest side is times the length of a leg.
24. THE UNIT CIRCLE For angle measures greater than 90 deg, we use REFERENCE ANGLES.
25. Reference angles Angle rotation starts from the positive x-axis, then moving counter-clockwise. The reference angle is measured from the x-axis. What is the reference Angle of the ff? 1.) 120 deg = 2.) 225 deg = 3.) 330 deg =
