Given a function and both a vertical and a horizontal shift, sketch the graph.
Identify the vertical and horizontal shifts from the formula.
The vertical shift results from a constant added to the output. Move the graph up for a positive constant and down for a negative constant.
The horizontal shift results from a constant added to the input. Move the graph left for a positive constant and right for a negative constant.
Apply the shifts to the graph in either order.
Graphing combined vertical and horizontal shifts
Given
sketch a graph of
The function
is our toolkit absolute value function. We know that this graph has a V shape, with the point at the origin. The graph of
has transformed
in two ways:
is a change on the inside of the function, giving a horizontal shift left by 1, and the subtraction by 3 in
is a change to the outside of the function, giving a vertical shift down by 3. The transformation of the graph is illustrated in
[link] .
Let us follow one point of the graph of
The point
is transformed first by shifting left 1 unit:
The point
is transformed next by shifting down 3 units:
Identifying combined vertical and horizontal shifts
Write a formula for the graph shown in
[link] , which is a transformation of the toolkit square root function.
The graph of the toolkit function starts at the origin, so this graph has been shifted 1 to the right and up 2. In function notation, we could write that as
Using the formula for the square root function, we can write
Graphing functions using reflections about the axes
Another transformation that can be applied to a function is a reflection over the
x - or
y -axis. A
vertical reflection reflects a graph vertically across the
x -axis, while a
horizontal reflection reflects a graph horizontally across the
y -axis. The reflections are shown in
[link] .
Vertical and horizontal reflections of a function.
Notice that the vertical reflection produces a new graph that is a mirror image of the base or original graph about the
x -axis. The horizontal reflection produces a new graph that is a mirror image of the base or original graph about the
y -axis.
Reflections
Given a function
a new function
is a
vertical reflection of the function
sometimes called a reflection about (or over, or through) the
x -axis.
Given a function
a new function
is a
horizontal reflection of the function
sometimes called a reflection about the
y -axis.
Given a function, reflect the graph both vertically and horizontally.
Multiply all outputs by –1 for a vertical reflection. The new graph is a reflection of the original graph about the
x -axis.
Multiply all inputs by –1 for a horizontal reflection. The new graph is a reflection of the original graph about the
y -axis.
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
it starts up serve and return practice/assessments.it helps find voice talking therapy also assessments through relaxed conversation.
miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills
hello. autism is a umbrella term. autistic kids have different disorder overlapping. for example. a kid may show symptoms of ADHD and also learning disabilities.
before treatment please make sure the kid doesn't have physical disabilities like hearing..vision..speech problem. sometimes these
Jharna
continue..
sometimes due to these physical problems..the diagnosis may be misdiagnosed.
treatment for autism.
well it depends on the severity.
since autistic kids have problems in communicating and adopting to the environment.. it's best to expose the child in situations where the child
Jharna
child interact with other kids under doc supervision.
play therapy.
speech therapy.
Engaging in different activities that activate most parts of the brain.. like drawing..painting. matching color board game.
string and beads game.
the more you interact with the child the more effective
Jharna
results you'll get..
please consult a therapist to know what suits best on your child.
and last as a parent. I know sometimes it's overwhelming to guide a special kid.
but trust the process and be strong and patient as a parent.
Jharna
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