section 1.6 - find all x - values where the function is discontinuous.\n2) $f(x)=\frac{-2x}{(7x - 7)(2…

Explanation:

Step1: Recall discontinuity condition

A rational function $\frac{g(x)}{h(x)}$ is discontinuous where $h(x)=0$. For a polynomial, it is continuous everywhere.

Step2: Find discontinuities of $f(x)$

Set the denominator of $f(x)=\frac{-2x}{(7x - 7)(2 - 8x)}$ equal to 0. $(7x - 7)(2 - 8x)=0$. Using the zero - product property, if $ab = 0$, then $a = 0$ or $b = 0$. For $7x-7 = 0$, we have $7x=7$, so $x = 1$. For $2-8x=0$, we have $8x=2$, so $x=\frac{1}{4}$.

Step3: Analyze $y=x^{2}+8x - 5$

Since $y=x^{2}+8x - 5$ is a polynomial function (a quadratic polynomial), it is continuous for all real $x$, i.e., there are no discontinuities.

Answer:

The function $f(x)=\frac{-2x}{(7x - 7)(2 - 8x)}$ is discontinuous at $x = 1$ and $x=\frac{1}{4}$. The function $y=x^{2}+8x - 5$ has no discontinuities.