Given:
[tex]f(x)=\frac{1}{3} x-3[/tex]
[tex]g(x)=3 x-3[/tex]
[tex]p(x)=-3 x+3[/tex]
[tex]3 h(x)=x[/tex]
To find:
Which function has a graph that intersects the y-axis at 3.
Solution:
General form of equation of a line:
y = mx + c
where "y" is the function, "m" is the slope and "c" is the y-intercept.
Option A: [tex]f(x)=\frac{1}{3} x-3[/tex]
y-intercept of this function is -3.
It is not true.
Option B: [tex]g(x)=3 x-3[/tex]
y-intercept of this function is -3.
It is not true.
Option C: [tex]p(x)=-3 x+3[/tex]
y-intercept of this function is 3.
It is true.
Option D: [tex]3 h(x)=x[/tex]
y-intercept of this function is 0.
It is not true.
Therefore [tex]p(x)=-3 x+3[/tex] has a graph that intersects the y-axis at 3.
