sino maka pag answer nito plss assignment ko kasi tapus wrong pa yung answer ko
Answer (1)
ANSWER:1.) f(x) = (2x + 3)/(x − 1): VA at x = 1, HA at y = 2, x-int (−3/2, 0), y-int (0, −3).2.) f(x) = (x − 3)/(x² − 1): VAs at x = −1 and x = 1, HA at y = 0, x-int (3, 0), y-int (0, 3).STEP-BY-STEP EXPLANATION: Graph 1: 1. Vertical Asymptote (VA)The denominator becomes 0 at .Rational functions “blow up” near these points, creating a vertical asymptote.On the graph: the dashed vertical line at .2. Horizontal Asymptote (HA)The numerator and denominator have the same degree (1).Divide leading coefficients: .This means as , approaches .On the graph: the dashed horizontal line at .3. x-interceptWhere , numerator = 0: → .Point: (marked with an X on the x-axis).4. y-interceptWhere , .Point: (marked on the y-axis).Graph 2: 1. Vertical Asymptotes (VA)Denominator factors: .Denominator = 0 at and .So, two vertical asymptotes: dashed lines at and .2. Horizontal Asymptote (HA)Degree of numerator (1) < degree of denominator (2).Rule: if degree numerator < degree denominator → HA at .Dashed horizontal line along the x-axis.3. x-interceptNumerator = 0: → .Point: on the x-axis.4. y-interceptPoint: on the y-axis. Why the graphs look like thatVertical asymptotes split the graph into separate sections because the function is undefined there.Horizontal asymptotes show where the graph flattens out far to the left and right.Intercepts are where the graph touches or crosses the axes.If you imagine walking along the curve, you’d see it climb steeply toward infinity near a vertical asymptote, level off toward the horizontal asymptote far away, and pass exactly through its intercept points.PABRAINLEST PO THAKKS
