Rational Functions and Their Discontinuities and Intercepts

h(x)=x²+4x-32 / x²-8x+16
At each of the following values of x, select whether h has a zero, a vertical asymptote, or a removable discontinuity.

• x=-8 is a zero and x=4 is a vertical asymptote
• x=-8 is a zero and x=4 is a removable discontinuity
• x=-8 is a zero and x=4 is a zero
• x=8 is a zero and x=-4 is a vertical asymptote

Tags

CCSS.HSF-IF.C.7D

g(x)=x²-2x-24 / x²+10x+24 
At each of the following values of x, select whether g has a zero, a vertical asymptote, or a removable discontinuity. 

• x=6 is a vertical, x=4 is a removal discontinuity, and x=-6 is a zero.
• x=-6 is a vertical asymptote, x=-4 is a removal discontinuity, and x=6 is a zero.
• x=-6 and x=6 is a zero and  x=4 is a vertical asymptote.
• x=-6 and x=4 is a zero and x=6 is a vertical asymptote.

Tags

CCSS.HSF-IF.C.7D

p(x)=x²-3x-40 / x²+16x+64
At each of the following values of x, select whether p has a zero, vertical asymptote, or a removable discontinuity.

• x=-8 and 8 is a vertical asymptote and x=-5 is a zero.
• x=-5 and x=-8 is a zero and x=8 is a vertical asymptote.
• x=-8 is a vertical asymptote and x=-5 and x=8 is a zero.
• None of the above

Tags

CCSS.HSF-IF.C.7D

Define the word asymptote.

• Where a line that crosses the y axis.
• A value that you get closer to, but never quite reach.
• Where a line that crosses the x axis.
• End behavior that goes to infinity on either side

Tags

CCSS.HSF-IF.C.7D

o(x)=x²-81 / x+9
At each of the following values of x, select whether o has a zero, a vertical asymptote, or a removable discontinuity.

• x=9 and x=-9 is a zero.
• x=9 is a zero and x=9 is a removable discontinuity.
• x=9 is a removable discontinuity and x=-9 is a zero.
• x=9 is a zero and x=-9 is a removable discontinuity.

Tags

CCSS.HSF-IF.C.7D