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Part C: Communication (20 marks) 1. Let f(x) = x + 3 and g(x) = x2...
Question 1 The functions f(x) g(x) and h(x) are defined as follows: f(x) = e* XER g(x) = x x 20 h(x) = 2x + 1 XER [3 marks] Find fg(x) and state its domain and range Find hf (x) and state its domain and range Find hº(x) and state its domain and range __[3 marks] (1111) [3 marks] WA (b) The figure below shows the graph of y=-x-shifted to four new positions. Write an equation for each new graph....
please show work 1.Let g(x) = log3(x +3)-1 . d. (3 pts) f(8)-3, the corresponding point on the graph of f(x)is.H The transformed point on the graph of g(x) is . e. (2 pts) Find the domain and the range. Write in interval notation. 1d. point on f(x): point on g(x): f. (1 pt) What is the vertical asymptote? That is, as x→ 1e. D: R: 1f. 8. (5 pts) Find the equation of the inverse, g(x). 1g. 1.Let g(x)...
1+1 5. [10 marks) Find all values of k such that f(x) = -r2 + 2kr +1" has domain (-0,0). 6. [10 marks] Sketch the graph of y = -2 -2 log: (2-2) and find its domain, range, -intercept and y-intercept. Show your transformations step by step. 7. (12 marks] (a) [8 marks) Find the equation of the tangent line to the graph of the function f(x) = 3.0" - 6x2 - 7 at = 2 (b) (4 marks) Find...
4. Continuing with problem 3, f(x) = 2x? + 8x + 5. a) Find the x and y intercepts. b) Give the domain of the function. c) Give the range of the function. d) Sketch the graph of the function.
Let f(x) = x + 5 and g(x) = x2 + 9x + 20. Determine a simplified algebraic model for y = 96) and identify its domain.
Let f(x) = x2 - 5 and g(x) = 6x + 1. Find the function. fog (f.g)(x) = Find its domain. (Enter your answer using interval notation.)
g) Sketch the graph of f(x) h) Determine the minimum or maximum value of the function. i) State the domain and the range in interval notation. 1. Given f(x)-2-3x (7 points) a) State whether the graph of the parabola opens upward or downward. b) Identify the vertex using the vertex formula. c) Determine the x-intercepts d) Determine the y-intercept. e) Determine the axis of symmetry ) Write the equation of the function fit) in vertex forrm g) Sketch the graph...
5. Sketch the function that has a graph the shape of s(x) = x2, with a horizontal shrink by a factor of and shifted up two units. Write the equation of the function. State the domain of the transformed function in interval notation. Five Centered Coordinates of Basic Function LX f(x) Equation: Domain:
I need these questions all solved please. (11) Let f(x) x3 - 1 and g(x) = 25 sin 3r (a) What is the range of g(f(x))? Justify your answer (b) If h(r) f(g(x)) compute h'(x) (c) If t(x) ef(r) compute t'(x). (d) Obtain f'() from first principles 6 marks 6 marks 6 marks 6 marks 3. (e) Obtain the equation of the line tangent to the curve y [6 marks f(x) at (12) In this question, f(x)= r+2)2 2r (a)...
Question 8 (6 marks) Consider the function f: [-2, 2] shown in the diagram. R whose graph is (a) State the largest intervals on which f is injective f(z) (b) For each interval I you found in (a), sketch the graph of the inverse g of the restriction of f to I and state the domain and range of g (c) If we know that f(-x) = f(x) for all r e dom(f), what can we conclude about the relationship...