If [tex]$g(x)=3x$[/tex] is graphed on a coordinate plane, what is the [tex]$y$[/tex]-intercept of the graph?
Answer (2)
To find the y -intercept of the function g ( x ) = 3 x , we set x = 0 .
Calculate g ( 0 ) = 3 × 0 = 0 .
The y -intercept is the value of the function when x = 0 .
The y -intercept is 0 .
Explanation
Understanding the Problem We are given the function g ( x ) = 3 x and asked to find the y -intercept of its graph. The y -intercept is the point where the graph intersects the y -axis. This occurs when x = 0 .
Finding the y-intercept To find the y -intercept, we need to evaluate the function g ( x ) at x = 0 . So we calculate g ( 0 ) .
Calculating g(0) We have g ( 0 ) = 3 ( 0 ) = 0 . Therefore, the y -intercept is 0.
Stating the Answer The y -intercept is the point ( 0 , 0 ) . The y -coordinate of this point is the y -intercept, which is 0.
Examples
Imagine you're tracking the distance a car travels over time, where the distance d is given by d = 3 t , with t being the time in hours. The y -intercept represents the initial distance at time t = 0 . In this case, the y -intercept is 0, meaning the car starts at a distance of 0 miles from the starting point. Understanding intercepts helps in interpreting real-world scenarios like this, providing a clear starting point for the relationship between two variables.
The y -intercept of the function g ( x ) = 3 x is found by evaluating the function at x = 0 , which gives g ( 0 ) = 0 . Thus, the y -intercept is 0, and the point of intersection with the y -axis is at (0, 0).
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