An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

h ( x ) has the lowest minimum value of -9.
f ( x ) has an x-intercept at x = − 1 and a y-intercept at f ( 0 ) = 1 .
g ( x ) has an x-intercept at x = 3 and a y-intercept at g ( 0 ) = − 3 .
h ( x ) has an x-intercept at x = 0 and a y-intercept at h ( 0 ) = 0 . Therefore, f ( x ) , g ( x ) , and h ( x ) all have both x- and y-intercepts. f ( x ) , g ( x ) , h ( x ) ​

Explanation

Analyzing the Problem We are given a table of values for three functions: f ( x ) , g ( x ) , and h ( x ) . Our goal is to analyze these functions based on their minimum values and intercepts to complete the given sentences.

Finding Minimum Values First, let's identify the minimum value of each function from the table:



For f ( x ) , the values are 0, 1, 2, 3. The minimum value is 0.
For g ( x ) , the values are -4, -3, 0, 5. The minimum value is -4.
For h ( x ) , the values are 7, 0, -9, 16. The minimum value is -9.

Comparing the minimum values, we see that h ( x ) has the lowest minimum, which is -9.

Identifying Intercepts Next, let's identify the x- and y-intercepts for each function:


x-intercept: A point where the function's value is 0.

y-intercept: The value of the function when x = 0 .

For f ( x ) :

x-intercept: f ( x ) = 0 when x = − 1 .
y-intercept: f ( 0 ) = 1 .
f ( x ) has both x- and y-intercepts.


For g ( x ) :

x-intercept: g ( x ) = 0 when x = 3 .
y-intercept: g ( 0 ) = − 3 .
g ( x ) has both x- and y-intercepts.


For h ( x ) :

x-intercept: h ( x ) = 0 when x = 0 .
y-intercept: h ( 0 ) = 0 .
h ( x ) has both x- and y-intercepts.




Final Answer From the analysis above, we can conclude:


h ( x ) has the lowest minimum.
All three functions, f ( x ) , g ( x ) , and h ( x ) , have both x- and y-intercepts.

Examples
Understanding functions and their properties like minimum values and intercepts is crucial in many real-world applications. For example, in business, a function might represent the profit of a company. Finding the minimum value helps identify the point where the company is losing the most money. Intercepts can show when the company breaks even (x-intercept) or the initial investment (y-intercept). Analyzing these properties helps in making informed decisions to improve the business's performance.

Answered by GinnyAnswer | 2025-07-04

The total charge that flows through the device is 450 C, and this corresponds to approximately 2.81 × 10^21 electrons flowing through it in 30 seconds.
;

Answered by Anonymous | 2025-07-18