Assignment
Question 1. Which of the following functions are linear or quadratic? If a function is linear, what is its slope and its y-intercept? Is it increasing or decreasing? If a function is quadratic, is it concave up or concave down?
(a) y = (x - 5)2 - 7,
(b) y = (x + 3)3 - 1,
(c) y = 3x - 19,
(d) y = -8 + (3x2 - 1)(1 + x),
(e) y = -x2 + 4x - 2/3,
(f) y = 5/2 x + x2,
(g) y - 7 - x2 = x,
(h) y = 99.
Question 2. Sketch the graph of the function y = 3x - 6. Write the formula for the inverse of this function and sketch the graph of the inverse in the same coordinate system.
Question 3. A straight line passes through the points (-1, 5) and (1, -2). Find the equation of the straight line.
Question 4.
(a) Sketch the graph of the function y = x2.
(b) Sketch the graph of the function y = (x + 1)2.
(c) Sketch the graph of the function y = (x + 1)2 - 3.
(d) Give the coordinates of the vertex of the parabola from part (c).
(e) Convert the vertex form from part (c) into the general form of a quadratic function.
Question 5. Is the function y = 9x2, defined on the domain R with the codomain [0, ∞), invertible? Will it be invertible if we restrict the domain to the interval [0, ∞)? If not, explain why. If yes, write the formula for the inverse function.
Question 6. Solve the equation x2 - 5x + 6 = 0.
Question 7. Find the vertex of the parabola
y = -x2 + 5x - 6.
Is the vertex the maximum or the minimum of this quadratic function?