Targeted Philippine Basic Education Curriculum Competencies
High School Mathematics IV: Advanced Algebra, Trigonometry, and Statistics

Linear Functions

1. Define the linear function f(x) = mx + b; given a linear function Ax + By = C, rewrite in the form f(x) = mx + b and vice versa.
2. Draw the graph of a linear function given the following:
   • any two points
   • slope and one point
   • slope and the y-intercept
   • x and y intercepts

Quadratic Functions

1. Define a quadratic function f(x) = ax² + bx + c; identify quadratic functions.
2. Rewrite a quadratic function ax² + bx + c in the form f(x) = a(x-h)² + k and vice versa.
3. Given a quadratic function, determine:
   • highest or lowest point (vertex)
   • axis of symmetry
   • direction of opening of the graph
4. Draw the graph of a quadratic function using the vertex, axis of symmetry, and assignment of points.
5. Analyze the effects on the graph of changes in 'a', 'h' and 'k' in f(x) = a(x-h)² + k

Exponential and Logarithmic Functions

1. Define the exponential function f(x) = a^x and differentiate it from other functions studied earlier; given a table of ordered pairs, state whether the trend is exponential or not.
2. Draw the graph of an exponential function f(x) = a^x and describe some properties of the function or its graph.
   • a > 1
   • 0 < a < 1
3. State the domain, range, intercepts and trend (increasing and decreasing) of a given exponential function based on its graph.

Student Objectives/Learning Outcomes
At the end of the unit, students will be able to: 

1. graph functions and give their domain and range;
2. research about a famous Muslim mathematicians and his/her contributions to mathematics and report it using a multimedia presentation;
3. make conjectures on the effect of 
   • 'k' on linear function y = x± k and on quadratic function y = x² ± k.
   • ‘P’, ‘a’, and ‘k’ on the graph y = Pa^kx. 
   • 'a' on the graph y = log_ax.
4. find the inverse of a function using reflection of graphs;
5. investigate transformation concepts used in Muslim textiles; 
6. create designs using transformations
   • identify the different functions and their graphs
   • graph functions using translation;
7. promote their designs using a brochure;
8. value one’s cultural heritage; and
9. appreciate mathematics in designs and crafts.