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 Find the listed information for the rational function. (x+2)(x+1) f(x) = = (x+2)(x-3) (x+1)3 Reduced f(x) = (x-3) Domain: # -2,3 Vertical Asymptote(s): There is/are vertical asymptote(s) at x=3 There are no vertical asymptotes. The VA is even. The VA is odd. There is no VA. Hole(s): There is a hole at (-2,-115) There is no hole in the function. The degree of the x-intercept is even, meaning the graph will bounce on it. The degree of the x-intercept is odd, meaning the graph will cross the x-axis at the intercept. There is no a-intercept. y-intercept: There is a y-intercept(s) at There are no y-intercepts. End Behavior: O There is a HA at 07 07 Submit Question (") 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+ Show complete work on your worksheet! x-9 f(x): = -x- 12 Reduced function: fred(2) Domain: Select an answer VA: There is/are vertical asymptote(s) at There are no vertical asymptotes. Hole(s): O There is a hole at There is no hole in this function. x-intercept(s): There is/are -intercept(s) at There are no x-intercepts. y-intercept: There is a y-intercept(s) at There are no y-intercepts. End Behavior: End Behavior: O There is a horizontal asymptote at 0 My graph looks like this. (You do NOT need to plot the hole here in Canvas but make sure that it is on the graph on your worksheet.) 7+ 6- 5- 4 3- 2 1 -5 -4-3 -2 -1 2 3 4 5 -1 -2 -3 -4 -5+ Clear All Draw: