graphing functions

Question 1

features of y= 1/f(x) in relation to
y= f(x)

Answer 1

• vertical asymptotes of f(x) becomes roots of 1/f(x)
• roots of f(x) becomes vertical asymptote of 1/(fx)
• y-intercept -> 1/y-int
• horizontal asymptote: 1/h.a.
• (a,b) turning point of f(x) becomes the opposite turning point (a, 1/b)

Question 2

features of y=[f(x)]ˆ2 in relation to y=f(x)

Answer 2

• y<0 in y=f(x) becomes y>0 in f(x)ˆ2
• root becomes local minimum
• y intercept (0, b) becomes y intercept at (0, bˆ2)
• vertical asymptote is unchanged
• horizontal asymptote y=a, becomes y=aˆ2

Question 3

y= f(|x|)

Answer 3

reflect on the y-intercept

Question 4

y =f(|x|-1)

Answer 4

reflect on the line of the root (as if it were an asymptote), plus horizontal translation to the right by 1

Question 5

y= |f(x)|

Answer 5

reflect on x-axis, but only reflect the negative part, so that y values are positive.

Question 6

y= |f(x-1)|

Answer 6

reflect on y-intercept plus horizontal translation to the right by 1

Question 7

y= f(2x)

Answer 7

divide x values by 2

Question 8

y= (f(x))/2

Answer 8

divide y values by 2

Question 9

y= -f(x)

Answer 9

reflection in the x-axis

Question 10

y= f(-x)

Answer 10

reflection in the y-axis

Question 11

odd and even functions formulas

Answer 11

even: f(-x) = f(x)
odd: -f(x)= f(-x)