The question wants us to find the y-intercept for the following function:
![f(x)=x^4+3x^3-2x+7](https://img.qammunity.org/2023/formulas/mathematics/college/k8dgh1d9yz4wh2otlao9t30zxbp6vimk4c.png)
To find the y-intercept, we just need to evaluate the function on the y-axis( x = 0). Doing the evaluation:
![\begin{gathered} f(0)=0^4+3*0^3-2^{}*0+7=7^{} \\ \Rightarrow f(0)=7 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/a1e89t7v3ua4q5x9axrmbs6izkc588gq94.png)
With this, we find that the function intercept the y-axis at the point (0, 7).
The answer is:
![(0,7)](https://img.qammunity.org/2023/formulas/mathematics/college/yeb2yty1javqucx14ixxcxgkob3fl1meb7.png)