Answer【Answer】: 1.C 2.E 3.G 4.I 5.L 6.V 7.Y II. Representation by graphs, tables, and equations; horizontal asymptote is y=-1;x-intercepts are at x=2; y-intercepts are at y=-1.
【Explanation】:
Working through these one at a time:
1. Solve `(x+2)/3=(2x-4)/2`, by cross-multiplication we can transition the problem into `2x+4=6x-12`, and solve the equation we will get x=-1 on reduce form. and substituting it again in the equation results x=-1 or x=2.choosing Option C as the answer.
2. Similar steps can be applied to solution 2.The Equation `7/4x-3/x^2=1/2x^2` solves to give the ordered pair `(2,11/2)`, hidden in option E.
3. Solving `(x^2-1)/(x-3)=8/(x-3)` over the domain of real numbers excluding three gives x= 4, So option G
4. Determine `(x^2-1)/(x-3)=8/(x-3)`, reveals x=3 , leading us to choose option I
5. Evaluate `1/(x-6)+x/(x-2)=4/(x^2-8x+12)` and cross multiply we can get `(-4,1)`. The correct answer choice is L.
6. Determine `5x/(x-1)<4`, we are able to see that this gives us option V.
7. Solve `x/(x-2)-7=2/(x-2)` leads to the solution (-Infinity,-4)U(1,3) which corresponds to choice Y in the given options.
Now tackling the question about the rational function, Its representations directly involve:
• Through a graph: Depending on the situation, direct substitution will help you find one / a set of "acceptable" solutions. If a bunch / broader marks (e.g. (infinity, 4)) are needed, sketching the graph based on understanding its 'behaviors' like asymptotes and points of discontinuity will be much indirect, but useful.
• Through a table of values.
• Through its Equation Representation
Bear the facts - this function cannot take all real numbers as input (notably: -2), and its highest/exponent leading term deals with different growth rates between polynomial (aka certain trends of the function ). Based on all above, there would also be one effective attribute arriving, which isn't explicitly posed just with number or operation use. Together all these three incorporate so much symmetry for us to snapshot this function efficiently, providing better sense beyond simple direct computation,
Answers & Comments
Answer:
Answer【Answer】: 1.C 2.E 3.G 4.I 5.L 6.V 7.Y II. Representation by graphs, tables, and equations; horizontal asymptote is y=-1;x-intercepts are at x=2; y-intercepts are at y=-1.
【Explanation】:
Working through these one at a time:
1. Solve `(x+2)/3=(2x-4)/2`, by cross-multiplication we can transition the problem into `2x+4=6x-12`, and solve the equation we will get x=-1 on reduce form. and substituting it again in the equation results x=-1 or x=2.choosing Option C as the answer.
2. Similar steps can be applied to solution 2.The Equation `7/4x-3/x^2=1/2x^2` solves to give the ordered pair `(2,11/2)`, hidden in option E.
3. Solving `(x^2-1)/(x-3)=8/(x-3)` over the domain of real numbers excluding three gives x= 4, So option G
4. Determine `(x^2-1)/(x-3)=8/(x-3)`, reveals x=3 , leading us to choose option I
5. Evaluate `1/(x-6)+x/(x-2)=4/(x^2-8x+12)` and cross multiply we can get `(-4,1)`. The correct answer choice is L.
6. Determine `5x/(x-1)<4`, we are able to see that this gives us option V.
7. Solve `x/(x-2)-7=2/(x-2)` leads to the solution (-Infinity,-4)U(1,3) which corresponds to choice Y in the given options.
Now tackling the question about the rational function, Its representations directly involve:
• Through a graph: Depending on the situation, direct substitution will help you find one / a set of "acceptable" solutions. If a bunch / broader marks (e.g. (infinity, 4)) are needed, sketching the graph based on understanding its 'behaviors' like asymptotes and points of discontinuity will be much indirect, but useful.
• Through a table of values.
• Through its Equation Representation
Bear the facts - this function cannot take all real numbers as input (notably: -2), and its highest/exponent leading term deals with different growth rates between polynomial (aka certain trends of the function ). Based on all above, there would also be one effective attribute arriving, which isn't explicitly posed just with number or operation use. Together all these three incorporate so much symmetry for us to snapshot this function efficiently, providing better sense beyond simple direct computation,