The distance between the y-intercept of the function f and the y-intercept of the function g is 9 units. The answer is D. 9 units.
The y-intercept of a function is the point of intersection between the function's graph and the y-axis. The y-axis is also known as the x=0 line, since every point on the y-axis has an x-value of 0.
To find the y-intercept of the function f, we can set x=0 and evaluate the function. f(0)=2(0)^2-6(0)+3=3. This means that the y-intercept of the function f is (0,3).
To find the y-intercept of the function g, we can find the equation of the function and then set x=0 and evaluate. The table of values for the function g is given below:
x g(x)
-5 15
-2 3
2 13
5 25
Based on the table of values, we can see that the function g is a linear function. The equation of a linear function can be written in the form y=mx+b, where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we can use the formula m=(y2-y1)/(x2-x1), where y1 and y2 are any two y-values of the line, and x1 and x2 are the corresponding x-values.
Using the table of values, we can choose the points (-5,15) and (2,13) to find the slope. m=(13-15)/(2-(-5))=1/3.
To find the y-intercept, we can plug in the slope and any point from the table into the equation y=mx+b. Using the point (2,13), we get 13=(1/3)(2)+b. Solving for b, we get b=12.
This means that the equation of the function g is y=(1/3)x+12. To find the y-intercept, we can set x=0 and evaluate. g(0)=(1/3)(0)+12=12. This means that the y-intercept of the function g is (0,12).
The distance between the y-intercept of the function f and the y-intercept of the function g is the absolute difference between their y-values. The y-value of the y-intercept of the function f is 3, and the y-value of the y-intercept of the function g is 12. The absolute difference between these two values is |12-3|=9.
Therefore, the distance between the y-intercept of the function f and the y-intercept of the function g is 9 units. The answer is D. 9 units.