Which graph shows h of x is equal to f of x over g of x ?
Answer
A
Image with description On a coordinate plane, the x and y axes range from negative 10 to 10 in increments of 5. The graph has a parabola (h of x), a straight line (g of x), and smooth curves (f of x). The parabola (h of x) has a vertex at (0 comma negative 6) and passes close to (negative 2 point 5 comma 0). It has a hole close to (2 point 5 comma 0). The straight line (g of x) has a positive slope and passes close to (negative 2 point 5 comma 0) and (0 comma 2). One curve of (f of x) lies in the first quadrant and the other spreads in the third and fourth quadrants. The curve in the first quadrant has a horizontal asymptote at y equals 0. It goes in the positive direction of the x-axis and has a vertical asymptote at x approximately equal to 2 point 5. The other curve also has a horizontal asymptote at y equals 0, and it goes in the negative direction of the x-axis and has a vertical asymptote like the first curve.
B
Image with description On a coordinate plane, the x and y axes range from negative 10 to 10 in increments of 5. The graph has a parabola (f of x), and two straight lines (h of x), and (g of x). The parabola (f of x) that opens upwards has a vertex at (0 comma negative 6), and passes close to (negative 2 point 5 comma 0) and (2 point 5 comma 0). The straight line (h of x) has a positive slope and passes close to (2 point 5 comma 0). The straight line (g of x) also has a positive slope, and passes close to (negative 2 point 5 comma 0) and (0 comma 2).
C
Image with description On a coordinate plane, the x and y axes range from negative 10 to 10 in increments of 5. The graph has a parabola (f of x), a straight line (g of x), and smooth curves (h of x). The parabola (f of x) has a vertex at (0 comma negative 6) and passes close to (negative 2 point 5 comma 0). The straight line (g of x) has a positive slope and passes close to (negative 2 point 5 comma 0) and (0 comma 2). One curve of (h of x) lies in the first quadrant and the other spreads in the third and fourth quadrants. The curve in the first quadrant has a horizontal asymptote at y equals 0. It goes in the positive direction of the x-axis and has a vertical asymptote at x approximately equal to 2 point 5. The other curve also has a horizontal asymptote at y equals 0, and it goes in the negative direction of the x-axis and has a vertical asymptote like the first curve.
D
Image with description On a coordinate plane, the x and y axes range from negative 10 to 10 in increments of 5. The graph has a parabola (h of x), and two straight lines (f of x), and (g of x). The parabola (h of x) that open upwards has a vertex at (0 comma negative 6), and passes close to (negative 2 point 5 comma 0) and (2 point 5 comma 0). The straight line (f of x) has a positive slope and passes close to (2 point 5 comma 0). The straight line (g of x) also has a positive slope, and passes close to (negative 2 point 5 comma 0). It appears that (f of x) and (g of x) are parallel to each other.