Which of the following is TRUE about the transformation of function? 1. Vertical stretches or compressions always leave the x-intercepts of a function unchanged. 2. A vertical stretch by a factor of k means that the distance from any point on the graph to the x-axis is multiplied by k
Which of the following is TRUE about the transformation of function? 1. Vertical stretches or compressions always leave the x-intercepts of a function unchanged. 2. A vertical stretch by a factor of k means that the distance from any point on the graph to the x-axis is multiplied by k LS2019 发表于 2023-12-03 13:20
Which of the following is TRUE about the transformation of function? 1. Vertical stretches or compressions always leave the x-intercepts of a function unchanged. 2. A vertical stretch by a factor of k means that the distance from any point on the graph to the x-axis is multiplied by k LS2019 发表于 2023-12-03 13:20
😅，楼主问出这个问题没问题，下面解释就... What is a vertical stretch?When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.Given a function y=f(x), the form y=bf(x) results in a vertical stretch or compression. what is horizontal stretch or compression？ If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. Given a function y=f(x), the form y=f(bx)results in a horizontal stretch or compression. 选项 1，2 都说明了是vertical stretch，也就说明了是对谁变化。 实际上从严格数学定义出发，就只能乘以 positive number。要不就不是vertical stretch 楼主可以去问学校老师为什么不可以选 1? 如果学校老师说要考虑 0，那么你就直接 quote 数学书上的定义给他。严格的vertical stretch 有 b>0。不过有可能高中课本是简化版，有些类似商学院的统计课本，上面数学定义不是很严谨。 1，2 从定义来说都是对的。
😅，楼主问出这个问题没问题，下面解释就... What is a vertical stretch?When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.Given a function y=f(x), the form y=bf(x) results in a vertical stretch or compression. what is horizontal stretch or compression？ If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. Given a function y=f(x), the form y=f(bx)results in a horizontal stretch or compression. 选项 1，2 都说明了是vertical stretch，也就说明了是对谁变化。 实际上从严格数学定义出发，就只能乘以 positive number。要不就不是vertical stretch 楼主可以去问学校老师为什么不可以选 1? 如果学校老师说要考虑 0，那么你就直接 quote 数学书上的定义给他。严格的vertical stretch 有 b>0。不过有可能高中课本是简化版，有些类似商学院的统计课本，上面数学定义不是很严谨。 1，2 从定义来说都是对的。
Which of the following is TRUE about the transformation of function? 1. Vertical stretches or compressions always leave the x-intercepts of a function unchanged. 2. A vertical stretch by a factor of k means that the distance from any point on the graph to the x-axis is multiplied by k LS2019 发表于 2023-12-03 13:20
😅，楼主问出这个问题没问题，下面解释就... What is a vertical stretch?When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.Given a function y=f(x), the form y=bf(x) results in a vertical stretch or compression. what is horizontal stretch or compression？ If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. Given a function y=f(x), the form y=f(bx)results in a horizontal stretch or compression. 选项 1，2 都说明了是vertical stretch，也就说明了是对谁变化。 实际上从严格数学定义出发，就只能乘以 positive number。要不就不是vertical stretch 楼主可以去问学校老师为什么不可以选 1? 如果学校老师说要考虑 0，那么你就直接 quote 数学书上的定义给他。严格的vertical stretch 有 b>0。不过有可能高中课本是简化版，有些类似商学院的统计课本，上面数学定义不是很严谨。 1，2 从定义来说都是对的。
1. Vertical stretches or compressions always leave the x-intercepts of a function unchanged.
2. A vertical stretch by a factor of k means that the distance from any point on the graph to the x-axis is multiplied by k
改了 谢谢
如果 factor k=0 1） 不对。
你说1. 不对？
但是1.没有k
2
为什么1 不对？
why 1 is wrong?
楼上已经告诉你了 - 0倍的stretch
Stretch by 0 does not hold
那2. Stretch 0呢？
能问出这问题来，楼主不管是不是是挖坑的，我觉得大家都可以省省了。。。
碰到一个连1+1为什么等于2 都要你解释的人，你能给她讲清楚function的问题么？
y1=x1 - 1 intercept = 1
y2=2(x2 - 1) intercept = 2
therefore, #1 is wrong.
Well, be careful and think twice please.
说的是x-intercept，不是你说的这个y-intercept
我帮孩子问的。我是不懂。
你的孩子看了前面的回答，然后不懂，让你再来问么？
如果是，那么我的回答仍然成立。
如果不是，那么我建议你等你孩子看了回答，然后听你孩子说了之后，你再来问。不要自己不懂就自作主张问一些没有意义的问题。
1 绝大部分时候都不对，除了以 x 轴 为对称轴来 stretch 或 compress
比如一个 sine wave，如果保持低点不变，最高点不论是往上拉，还是往下压，x 轴上的零点肯定都得变。极端点，当 sinusoidal wave 的最高点 y 值小于 0 时，那所有的零点都消失了
这题默认的显然就是x 轴 为对称轴来 stretch 或 compress啊。
否则2也不可能对。
不是啊，方法 2 的确是限定了以 x 轴为 ‘对称轴’ 来延展，因为是 y‘ = y * k
方法 1 没有这样的限定，所以 1 不能普适成立
方法2 只提到graph上每一点到x-axis的距离，没有任何地方限定了以 x 轴为 ‘对称轴’ 来延展，更没说y‘ = y * k （只看原题，不要看别人的推导）。
我们认为是x 轴 为对称轴来 stretch 或 compress，就是因为如果不这么假定，这题就毫无意义而已。
What is a vertical stretch?When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression.Given a function y=f(x), the form y=bf(x) results in a vertical stretch or compression.
what is horizontal stretch or compression？ If the constant is between 0 and 1, we get a horizontal stretch; if the constant is greater than 1, we get a horizontal compression of the function. Given a function y=f(x), the form y=f(bx)results in a horizontal stretch or compression.
选项 1，2 都说明了是vertical stretch，也就说明了是对谁变化。 实际上从严格数学定义出发，就只能乘以 positive number。要不就不是vertical stretch 楼主可以去问学校老师为什么不可以选 1? 如果学校老师说要考虑 0，那么你就直接 quote 数学书上的定义给他。严格的vertical stretch 有 b>0。不过有可能高中课本是简化版，有些类似商学院的统计课本，上面数学定义不是很严谨。 1，2 从定义来说都是对的。
应该不能为0。
Vertical stretch or compression 只能乘以正数，定义里不包含0。那些说是因为0的不要误导人家娃。大于1 是stretch，0和1之间是compression。乘以负数那是叠加了reflection，不要误导别人。
x-intercept是f(x)=0，所以乘以任何正数，还是0。所以，x-intercept存在的情况下确实是不变的。 我觉得要么老师题出错了，要么他想说x intercept不存在的情况下不能算unchanged。
前面另一个说2（f(x)-1),那是stretch 叠加vertical shift。
所以1. 是对的，是吧？
这个定义实在是… 不过你说的对，可以问一下老师为什么1不对。
re 这个。 他们的stretches and shrinks 中的 k 是 positive real number。 所以两个都应该对。 楼主还是让孩子问问老师吧。