At y-intercept, the function intersect the y-axis means x coordinate is 0 and for x-intercept function intersect the x-axis and y-coordinate is 0.
Substitute 0 for f(x) in the equation to determine the x-intercept.
[tex]\begin{gathered} 0=3x+15 \\ x=-\frac{15}{3} \\ =-5 \end{gathered}[/tex]
The value of x is less than 1, so it satisfy the conditon x < 1.
[tex]\begin{gathered} 0=4x+14 \\ x=-\frac{14}{4} \\ =-\frac{7}{2} \end{gathered}[/tex]
Not possible as x must be greater or equal to 1.
So x-intercept of the function is (-5,0).
For y-intercept value of x is 0.
For x = 0, the possible function is f(x)= 3x +15.
Substitute 0 for x in the function to obtain the y-intercept.
[tex]\begin{gathered} f(0)=3\cdot0+15 \\ =15 \end{gathered}[/tex]
So y-intercept is (0,15).
At point of intersection both function become equal to each other. So,
[tex]\begin{gathered} 3x+15=4x+14 \\ 4x-3x=15-14 \\ x=1 \end{gathered}[/tex]
Substitute 1 for x in the equation f(x) = 4x + 14 to obtain the y coordinate for meet of curve.
[tex]\begin{gathered} f(1)=4\cdot1+14 \\ =4+14 \\ =18 \end{gathered}[/tex]
So point of meet is (1,18).
Thus correct option is second option.
x-intercept is (-5,0).
y-intercept is (0,15)
Point of intersection (meet) is (1,18).
