Where (for what values of a) does the rational function have (a) holes? (b) vertical asymptotes? Entry tip: Enter DNE if none. f(x)=-37- (x+28)(x+74) (x + 64)(x + 74)(x+8) Two copies of the same Rational Function are shown below. On the graph below draw the Horizontal Asymptote and write the equation for the horizontal asymptote underneath. f(x) = 5 4 3 2 1 -2 x- On graph below, draw the the Vertical Asymptote and write the equation for the Vertical Asymptote underneath. -2 f(x) = x- 5 4 3 2 1 -5 -4-3-2-1 1 2 3 -m -1 -2 -3 -4 Clear All Draw: -5 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 Clear All Draw: Horizontal Asymptote: y=0 Vertical Asymptote: x=1 Write an equation for a rational function with: Vertical asymptotes at x = 2 and x = 6 x-intercepts at x = -4 and x = -3 y-intercept at 8 y= Write an equation for a rational function with: Vertical asymptotes at x = 2 and x = 6 x-intercepts at x = 5 and x = -1 Horizontal asymptote at y = 8 y= Write an equation for the function graphed below 5 4 y= 32 -5-4-3-2 -1 I 2 3 4 5 6 7 -1 -2 -3 -4 -5- a Write an equation for the function graphed below 5 3 2+ 1 1 -L -2- -3 -7-6-5-4-3-2-1 y= -4 -5+ 2 -N + 3 4 5 6 7 a Write an equation for the function graphed below. The y intercept is at (0,0.4) 5 2 -7 -6 -5 -4 -2 -1 NY + + 2 3 4 5 6 7 -1 y= -4 -5- 2345 a Write an equation for the function graphed below 5 4 3 2 1 -7 -6 -5 -4 -2 -1 1 4 5 6 y= -2 -3 -4 -5+ Two copies of the same Rational Function are shown below. On the graph below draw the Horizontal Asymptote and write the equation for the horizontal asymptote underneath. f(x): = 1 x +3 On graph below, draw the the Vertical Asymptote and write the equation for the Vertical Asymptote underneath. -4 5+ 4 3 2 1 -2 -1 1 2 3 on -1 -2 -3 -4 -5 Clear All Draw: 4 10 1 f(x) = x+3 5 4 3 2 1 w 3 4 -4-3 -2 -1 1 2 -1 -2 -3 -4 -5+ Clear All Draw: Horizontal Asymptote: Vertical Asymptote: -10 9 Two copies of the same Rational Function are shown below. On the graph below draw the Horizontal Asymptote and write the equation for the horizontal asymptote underneath. f(x) = 10+ 99 3x x- 2 On graph below, draw the the Vertical Asymptote and write the equation for the Vertical Asymptote underneath. f(x) = 3x 2 x- 10+ 9 8 7 -6 5 4 3 8 7 6 sh 5 4 3 2 2 J 1 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 4 5 6 7 8 9 10 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -2 -3- -3 -4 4 -5- -5 -6- -6- -7 -7 -8- -8- -9 -9 10+ Clear All Draw: 10+ Clear All Draw: Horizontal Asymptote: Vertical Asymptote: -2x-1 Draw a graph of f(x) = -2 - 1 by first placing the horizontal and vertical asymptotes, then plotting an additional point on the graph. -5-4-3-2-1 Clear All Draw: 5 4 3 2 1 1 2 3 -1 -2 -3 -4 -5 to 4 5 Determine the end behavior of f(x): = -5x5 + 4x43x- 9x+8x+17 -5x3x+6x+5 Write an equation for the function graphed below 5+ 4 3 2 1 + -7 -6 -5 -4 -3-2-1 1 2 3 4 5 6 -1 y= -3 -4 -5+ Write an equation for the function graphed below 5+ 4 3 2 -7-6-5-4-3 -2 -1 2 3 5 6 7 -1 -2 -3 -4 -5 Write an equation for the function graphed below. The y intercept is at (0,0.4) 5+ 4 3 2 1+ -Z -6 -5 -4 -3 -2 1 2 3 4 5 6 7 -1 -3 -4 -5+