Question

Which function has the x-intercept and y-intercept at the same point?

A. f(x)=x³
B. f(x)=1/x​
C. f(x)=x−1
D. f(x)=1

Answer 1

The function which has both the x-intercept and y-intercept at the same point is f(x)=x³. The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the x-axis, then it is called the x-intercept. If a point crosses the y-axis, then it is called the y-intercept.

Step-by-step explanation:

The student has asked which function has the x-intercept and y-intercept at the same point. To solve this, we need to consider where each function crosses the x-axis (x-intercept) and the y-axis (y-intercept).

1. For f(x) = x³, the x-intercept is at x=0, because f(0) = 0³ = 0, and the y-intercept is also at y=0.
2. For f(x) = 1/x, the x-intercept does not exist as the function never touches the x-axis. The y-intercept also does not exist because as x approaches 0, 1/x approaches infinity.
3. For f(x) = x-1, the x-intercept is at x=1, because f(1) = 1-1 = 0, but the y-intercept is at y=-1 because f(0) = 0 - 1.
4. For f(x) = 1, there is no x-intercept because the function represents a horizontal line at y=1, which never crosses the x-axis. The y-intercept is at y=1.

Only the first option, f(x) = x³, has both intercepts at the same point (0, 0).

In Maths, an intercept is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept.