OPPapers.com

Algebra 133

MTH133 Unit 5 Individual Project Solutions

1) Find the domain of the following:

a)

Answer: All real numbers; (-∞,∞)

Explain how you obtained your answer here; from a sketch of the graph, from the definition of the exponential function – the fact that it is smooth and continuous and 5 can be raised to any power and yield something meaningful; answers may vary;

b)

Answer: All real numbers x > 4, (4, ∞)

Show your work or explain how you obtained your answer here: from a sketch of the graph; from the definition of the natural log; that it is well-defined only for non-negative x’s and this function is shifted to the right 4 units; answers may vary:

c)

Answer: All real numbers x > -2; (-2, ∞)

Explain how you obtained your answer here: from a sketch of the graph; from the definition of the natural log; that it is well-defined only for non-negative x’s and this function is shifted to the left 2 units; answers may vary :

d)

Answer: All real numbers; (-∞,∞)

Show your work or explain how you obtained your answer here: from a sketch of the graph, from the definition of the exponential function – the fact that it is smooth and continuous and e can be raised to any power and yield something meaningful answers may vary:

2) Describe the transformations on the following graph of. State the placement of the horizontal asymptote and y-intercept after the transformation. For example, left 1 or reflected about the y-axis are descriptions.

a)

Description of transformation: Subtracting a positive number from the original function gives a vertical shift downward; vertically shifts down 5 units

Equation(s) for the Horizontal asymptote(s): Horizontal asymptotes shift with any vertical shift (up or down) so y = -5 is the horizontal asymptote

y-intercept in (x, y) form: The point, (0, 1) is shifted down 5 units so (0, -4) is the new point

b)

Description of transformation: Taking the negative of the original function...