Questions: questions involving intervals, separate multiple answers by typing UNION to enter the U syn e:్ens more than one answer for a specific question, separate each answer from the following or ofanswer exists at all, enter NO SOLUTION. (a.) Enter as one or more points. x-intercept(s): (b.) Enter as a point. y-intercept:

questions involving intervals, separate multiple answers by typing UNION to enter the U syn e:్ens more than one answer for a specific question, separate each answer from the following or ofanswer exists at all, enter NO SOLUTION.
(a.) Enter as one or more points. x-intercept(s):
(b.) Enter as a point. y-intercept:

Transcript text: questions involving intervals, separate multiple answers by typing UNION to enter the $U$ syn e:్ens more than one answer for a specific question, separate each answer from the following or ofanswer exists at all, enter NO SOLUTION. (a.) Enter as one or more points. $\boldsymbol{x}$-intercept(s): (b.) Enter as a point. $y$-intercept: $\square$

Solution

Solution Steps

Solution Approach

To find the x-intercept(s) of a function, we need to determine the points where the function crosses the x-axis. This occurs when the y-value is zero. For the y-intercept, we need to find the point where the function crosses the y-axis, which occurs when the x-value is zero.

Step 1: Understanding the Problem

We need to find the $ x $-intercepts and $ y $-intercept of a given function. The problem does not specify the function, but we will assume it is a polynomial or a rational function for the sake of this example.

Step 2: Finding the $ x $-Intercepts

The $ x $-intercepts of a function are the points where the function crosses the $ x $-axis. This occurs when $ y = 0 $. To find the $ x $-intercepts, we set the function equal to zero and solve for $ x $.

Assume the function is $ f(x) = ax^2 + bx + c $.

Set $ f(x) = 0 $: \[ ax^2 + bx + c = 0 \]

Solve the quadratic equation using the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Step 3: Finding the $ y $-Intercept

The $ y $-intercept of a function is the point where the function crosses the $ y $-axis. This occurs when $ x = 0 $. To find the $ y $-intercept, we evaluate the function at $ x = 0 $.

For the function $ f(x) = ax^2 + bx + c $: \[ f(0) = a(0)^2 + b(0) + c = c \]