Question

A student graphs the piecewise function.3x + 15, x<14x+ 14,x >1 (this one has a line underneath it)Which characteristics will help the student graph the function correctly?

Answer 1

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.

`\begin{gathered} 0=3x+15 \\ x=-(15)/(3) \\ =-5 \end{gathered}`

The value of x is less than 1, so it satisfy the conditon x < 1.

`\begin{gathered} 0=4x+14 \\ x=-(14)/(4) \\ =-(7)/(2) \end{gathered}`

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.

`\begin{gathered} f(0)=3\cdot0+15 \\ =15 \end{gathered}`

So y-intercept is (0,15).

At point of intersection both function become equal to each other. So,

`\begin{gathered} 3x+15=4x+14 \\ 4x-3x=15-14 \\ x=1 \end{gathered}`

Substitute 1 for x in the equation f(x) = 4x + 14 to obtain the y coordinate for meet of curve.

`\begin{gathered} f(1)=4\cdot1+14 \\ =4+14 \\ =18 \end{gathered}`

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).