How do you know if a function has a tangent line?

Explanation: By solving the two equations you will get a point (x,y) which lies on both the curve and the straight line. if you got more than one point then this line will be intersecting and not a tangent to the curve. if it’s value is equal to the slope of the straight line then this line is its tangent.

How do you know if there is a horizontal tangent line?

A horizontal tangent line is a mathematical feature on a graph, located where a function’s derivative is zero. This is because, by definition, the derivative gives the slope of the tangent line. Horizontal lines have a slope of zero. Therefore, when the derivative is zero, the tangent line is horizontal.

Can a graph have more than one horizontal intercept?

Given the graph of any function, an x-intercept is simply the point, or points where the graph crosses the x-axis. There might be just one such point, no such point, or many, meaning a function can have several x-intercepts.

How many horizontal intercepts can the graph of a function have?

A graph can have many intercepts, one intercept, or no intercepts. If the graph is the graph of a function then it has at most one -intercept, since the graph of a function must pass the vertical line test and the y-axis is one such vertical line.

How do you find a tangent line on a graph?

1) Find the first derivative of f(x). 2) Plug x value of the indicated point into f ‘(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.

When tangent line is vertical?

The vertical tangent to a curve occurs at a point where the slope is undefined (infinite). This can also be explained in terms of calculus when the derivative at a point is undefined.

Can a line have 3 intercepts?

Explanation: It is possible for a line to have an infinite number of intercepts with the x or y -axis.

Can you have more than one intercept?

In answering these, remember that by definition, a function can only have one output (y-value) for each input (x-value). Therefore, it is not possible for a function to have more than one y-intercept.

How many vertical intercepts can the graph of a quadratic function have?

The graph of a quadratic function will always have one y-intercept and can have as many as two x-intercepts (recall that intercepts are points where a graph crosses an axis). The y-intercept is the point where the graph crosses the y-axis so it will be the value of the function at x = 0.

How many intercepts can a circle have?

Because a circle is round, it can cross the y-axis twice and have up to two y-intercepts.