Section 1.2

Question 1

When given roots and y-intercept of cubic to solve ax^3+bx^2+cx+d, how should you write it out before solving?

Answer 1

a((x-p)(x-q)(x-r)) Remember to find d via using y-intercept, then can be used to find a

Question 2

Reciprocal Graphs: Show graphs of k/x & k/x^2 for when k < 0 and k > 0 Draw and check myself

Answer 2

k/x, k > 0 k/x, k < 0 k/x^2, k > 0 k/x^2, k < 0

Question 3

For the reciprocal functions y = k/x and y = k/x² where k is a real constant, where are its asymptotes located?

Answer 3

x = 0

y = 0

Question 4

Sketch the reciprocal graphs for:

• y = k/x with k > 0
• y = k/x with k < 0
• y = k/x² with k > 0
• y = k/x² with k < 0

Answer 4

Question 5

Explain the transformation made when:

• y = f(x) + a
• y = f(x+a)
• y = af(x)
• y = f(ax)
• y = -f(x)
• y = f(-x)

Answer 5

y = f(x) + a is a translation of the graph y = f(x) vertically by the vector (0,a)

y = f(x+a) is a translation of the graph y = f(x) horizontally by the vector (-a,0)

y = af(x) is a stretch of the graph y = f(x) by scale factor a in the y-direction (vertical)

y = f(ax) is a stretch of the graph y = f(x) by scale factor of 1/a in the x-direction (horizontal)

y = -f(x) is a reflection of the graph y = f(x) in the x-axis

y = f(-x) is a reflection of the graph y = f(x) in the y-axis